From 9f987170dcdd191cf4d49caae89e0e036e96c114 Mon Sep 17 00:00:00 2001 From: Justin Phillips Date: Fri, 21 Apr 2023 16:27:59 -0700 Subject: [PATCH 1/2] rotating frames and hamiltonians update --- src/rotatingframes.jl | 184 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 184 insertions(+) create mode 100644 src/rotatingframes.jl diff --git a/src/rotatingframes.jl b/src/rotatingframes.jl new file mode 100644 index 0000000..7e28736 --- /dev/null +++ b/src/rotatingframes.jl @@ -0,0 +1,184 @@ +using QuantumOptics +using SparseArrays +export RotatingFrame +export rotatingphase +export unitary + +mutable struct RotatingFrame + chamber::Chamber + unitary::Vector{Float64} + + """ + In general, a change of basis to the Hamiltonian does not affect the underlying physics. Sometimes, such + a change of basis is beneficial computationally because if the change of basis itself is a function of + time, the frequency of temporal oscillations in the hamiltonian can be reduced (sometimes to zero). This + greatly simplifies the problem and improves computational speed. + + A rotating frame transformation may be thought of in terms of either operators or states acquiring time- + dependent phases. For experimentalists, it is often easiest to think of the phase as being attached to some + operator which appears in the Hamiltonian. For ion-trap experiments, those are most commonly a particular + projection operator (onto an atomic eigenstate) or a creation operator which acts on a vibrational mode. + + IonSim's RotatingFrame object keeps track of such time dependent phases that the user may choose to apply + in order to reduce the time dependence in their Hamiltonian. When constructing a Hamiltonian, a + RotatingFrame can be passed for this purpose. + + The RotatingFrame object should be interacted with through the use of operators, in agreement with the + philosophy outlined above, which are easily constructed natively by IonSim. The constructor then generates + a list of the phases which are applied to each eigenstate of the bare Hamiltonian and stores it in the + an attribute called unitary. + + The user constructs a RotatingFrame by passing a vector of tuples. + Each element of the vector has the form (operator, phase) where operator is an Operator type and phase is + a Float64. The Operator should be diagonal (either a projection operator of an atomoic state or the + number operator for a vibrational mode). For example, if the user wishes to apply the unitary U given by + + U(t) = exp(i * |S⟩⟨S| * ϕ₁t) × exp(i * a†a * ϕ₂t) + + then they should call + + RotatingFrame(chamber, [(|S⟩⟨S|, ϕ₁),(a†a, ϕ₂)]). + + Each of the operators needs to have the same dimensions as the Hamiltonian. This should be natively handled + properly by all of IonSim's operator construction functions. + """ + + function RotatingFrame(chamber::Chamber, + op_phase_tuples::Any + ) + @assert typeof(op_phase_tuples) <: Vector "Argument op_phase_tuples must be of type Vector." + hdim = length(basis(chamber)) + u = zeros(hdim) + + for (j,tup) in enumerate(op_phase_tuples) + @assert typeof(tup)<:Tuple{Operator,Float64} "Elements of op_phase_tuples must be of type Tuple{Operator,Float64}." + op = tup[1] + phase = tup[2] + @assert √(length(op))==hdim "Operator $j has incorrect dimensions." + for k in 1:hdim + u[k] = u[k] + phase*op.data[k,k] + end + end + + new(chamber, u) + end +end + +# Consider: T = X₁ ⊗ X₂ ⊗ ... ⊗ X_n (Xᵢ ∈ ℝ{dims[i]×dims[i]}), and indices: +# indxs[1], indxs[2], ..., indsx[N] = (i1, j1), (i2, j2), ..., (iN, jN). +# This function returns (k, l) such that: T[k, l] = X₁[i1, j1] * X₂[i2, j2] *...* X_N[iN, jN] +function get_kron_indxs(indxs::Vector{Tuple{Int64, Int64}}, dims::Vector{Int64}) + L = length(indxs) + rowcol = Int64[0, 0] + @assert indxs[L][1] <= dims[L] "indxs[$L][1] > dims[$L]" + @assert indxs[L][2] <= dims[L] "indxs[$L][2] > dims[$L]" + for i in 1:(L-1) + @assert indxs[i][1] <= dims[i] "indxs[$i][1] > dims[$i]" + @assert indxs[i][2] <= dims[i] "indxs[$i][2] > dims[$i]" + rowcol .+= prod(view(dims,(i+1):L)) .* (indxs[i] .- 1) + end + rowcol .+= indxs[L] + return rowcol +end + +# The inverse of get_kron_indxs. If T = X₁ ⊗ X₂ ⊗ X₃ and X₁, X₂, X₃ are M×M, N×N and L×L +# dimension matrices, then we should input dims=(M, N, L). +"""function inv_get_kron_indxs(indxs, dims) + row, col = indxs + N = length(dims) + ret_rows = Array{Int64}(undef, N) + ret_cols = Array{Int64}(undef, N) + for i in 1:N + tensor_N = prod(dims[i:N]) + M = tensor_N ÷ dims[i] + rowflag = false + colflag = false + for j in 1:dims[i] + jM = j * M + if !rowflag && row <= jM + @inbounds ret_rows[i] = j + row -= jM - M + rowflag = true + end + if !colflag && col <= jM + @inbounds ret_cols[i] = j + col -= jM - M + colflag = true + end + rowflag && colflag && break + end + end + return Tuple(ret_rows), Tuple(ret_cols) +end""" + +function rotatingphase(rf::RotatingFrame,sublvlindices::Vector{Int64},modeindices::Vector{Int64}) + @assert length(sublvlindices)≡length(ions(rf.chamber)) "Number of sublevel indices must match number of ions." + @assert length(modeindices)≡length(modes(rf.chamber)) "Number of mode occupation numbers must match number of modes." + ch = rf.chamber + indxs = Vector{Tuple{Int64,Int64}}() + dims = Vector{Int64}() + + for (i,ion) in enumerate((ions(ch))) + push!(dims,shape(ion)[1]) + end + + for (m,mode) in enumerate(modes(ch)) + push!(dims,shape(mode)[1]) + end + + for sublvlidx in (sublvlindices) + push!(indxs, (sublvlidx,sublvlidx)) + end + + for modeidx in modeindices + push!(indxs, (modeidx+1,modeidx+1)) + end + + dims = reverse(dims) + indxs = reverse(indxs) + + kron_idxs = get_kron_indxs(indxs,dims) + + return unitary(rf)[kron_idxs[1]] +end + +function rotatingphase(rf::RotatingFrame, σ::Any) + @assert typeof(σ) <: Operator "Must provide a transition operator." + (nzrows, nzcols, nzvals) = findnz(σ.data) + @assert length(nzrows) ≥ 1 "Must provide a nonzero operator." + return unitary(rf)[nzrows[1]] - unitary(rf)[nzcols[1]] +end + +function rotatingphase(rf::RotatingFrame, ionidx::Int64, transition::Tuple{Tuple{String, Rational},Tuple{String, Rational}}, modeidx::Int64, Δphonons::Int64) + ch = rf.chamber + allions = ions(ch) + allmodes = modes(ch) + sl1 = 0 + sl2 = 0 + for (i,sublevel) in enumerate(sublevels(allions[ionidx])) + if transition[1]==sublevel + sl1 = i + end + if transition[2]==sublevel + sl2 = i + end + end + sl1vector = [1 for i in 1:length(allions)] + sl1vector[ionidx] = sl1 + sl2vector = [1 for i in 1:length(allions)] + sl2vector[ionidx] = sl2 + + mode1vector = [0 for i in 1:length(allmodes)] + mode2vector = [0 for i in 1:length(allmodes)] + mode2vector[modeidx] = Δphonons + + return rotatingphase(rf, sl2vector, mode2vector) - rotatingphase(rf, sl1vector, mode1vector) +end + +function rotatingphase(rf::RotatingFrame, ionidx::Int64, transition::Tuple{Tuple{String, Rational},Tuple{String, Rational}}) + return rotatingphase(rf, ionidx, transition, 1, 0) +end + +function unitary(rf::RotatingFrame) + return rf.unitary +end \ No newline at end of file From 0e2b5c67a7f68fbab9a51da4f33c28c11d44798d Mon Sep 17 00:00:00 2001 From: Justin Phillips Date: Fri, 21 Apr 2023 16:31:46 -0700 Subject: [PATCH 2/2] rotating frames and hamiltonians update --- Project.toml | 3 + scrapwork/rotatingframes_examples.ipynb | 583 ++++++++++++++++++++++++ src/IonSim.jl | 1 + src/hamiltonians.jl | 88 +++- src/operators.jl | 126 +++++ test/runtests.jl | 1 + 6 files changed, 794 insertions(+), 8 deletions(-) create mode 100644 scrapwork/rotatingframes_examples.ipynb diff --git a/Project.toml b/Project.toml index d92df86..43bcd4e 100644 --- a/Project.toml +++ b/Project.toml @@ -4,6 +4,8 @@ authors = ["Joseph Broz "] version = "0.5.0" [deps] +CGcoefficient = "c862aa61-d51e-47d1-b396-b1e789b4e0b6" +DSP = "717857b8-e6f2-59f4-9121-6e50c889abd2" FunctionWrappers = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56" @@ -15,6 +17,7 @@ QuantumOptics = "6e0679c1-51ea-5a7c-ac74-d61b76210b0c" QuantumOpticsBase = "4f57444f-1401-5e15-980d-4471b28d5678" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" WignerSymbols = "9f57e263-0b3d-5e2e-b1be-24f2bb48858b" YAML = "ddb6d928-2868-570f-bddf-ab3f9cf99eb6" diff --git a/scrapwork/rotatingframes_examples.ipynb b/scrapwork/rotatingframes_examples.ipynb new file mode 100644 index 0000000..9f113a5 --- /dev/null +++ b/scrapwork/rotatingframes_examples.ipynb @@ -0,0 +1,583 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b66f944d", + "metadata": {}, + "source": [ + "# Example notebook: RotatingFrame" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d3188ee8", + "metadata": {}, + "outputs": [], + "source": [ + "using IonSim\n", + "using QuantumOptics: timeevolution, stochastic, Basis\n", + "import PyPlot" + ] + }, + { + "cell_type": "markdown", + "id": "6e1b9ae4", + "metadata": {}, + "source": [ + "# On-resonant Rabi flops" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3da5bf58", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "The core reason for the inclusion of rotating frames within IonSim is because the differential equation solver\n", + "is unable to find convergent solutions for rapidly time-varying hamiltonians. When constructed in the lab frame,\n", + "the hamiltonian for the case of a two-level atom being driven harmonically via its dipole interaction has the\n", + "form\n", + "\n", + " H = H₀ + H₁,\n", + "\n", + " H₁ = -d⃗⋅E⃗\n", + "\n", + "and if the dipole matrix element is real we can write (for levels |g⟩ and |e⟩)\n", + "\n", + " H₁ = -dE₀σₓ(e^(iνt)+e^(-iνt)).\n", + "\n", + "This has rapidly time-varying terms - the optical frequency ν is generally THz scale. We might be saved, \n", + "however, by the fact that we can make a unitary transformation U which depends on time such that our effective \n", + "Hamiltonian is given by\n", + "\n", + " H̃ = UHU† - iUU̇†.\n", + "\n", + "This is known as \"going into a rotating frame\". H̃ has terms with both slow (or sometimes zero) time \n", + "dependence, and terms with comparably fast time dependence. The fast-oscillating terms are generally then \n", + "thrown away as they quickly average to zero on the relevant timescales in what is known as the \"rotating wave \n", + "approximation.\" \n", + "\n", + "One could define U to be the diagonal matrix whose entries are \n", + "\n", + " U[j,j] = e^(-iEⱼt/ħ)\n", + "\n", + "where Eⱼ is the energy of the jᵗʰ eigenstate of the bare Hamiltonian H₀. This is known as the interaction\n", + "picture, and it is of much use for simulating nearly-resonantly-driven processes. In this picture, for a \n", + "two-level system, the slow-varying terms in the hamiltonian oscillate at the detuning of the drive frequency \n", + "from the transition frequency, Δ. Thus if Δ is small, the computational solver can find convergent solutions\n", + "in this rotating frame. What is important to keep in mind is that the interaction picture is itself a\n", + "rotating frame, and that it does not entirely eliminate time dependent terms even for a two-level system unless\n", + "the drive is perfectly resonant with the transition.\n", + "\n", + "Here, we will explore how to get useful, simulable Hamiltonians in IonSim, both when the process of interest\n", + "is driven near resonance, and when it is not.\n", + "\n", + "Let's define a two-level atom with a two-level vibrational mode, for a 4-dimensional Hilbert space.\n", + "\"\"\"\n", + "ca = Ca40([(\"S1/2\", -1/2, \"S\"), (\"D5/2\", -1/2, \"D\")])\n", + "laser = Laser()\n", + "chain = LinearChain(\n", + " ions=[ca],\n", + " comfrequencies=(x=3e6,y=3e6,z=1e6), \n", + " selectedmodes=(;z=[1])\n", + " )\n", + "\n", + "b = 4e-4\n", + "\n", + "chamber = Chamber(iontrap=chain, B=b, Bhat=ẑ, δB=0, lasers=[laser])\n", + "\n", + "#Set the vibrational Hilbert space to {0,1}.\n", + "modecutoff!(modes(chamber)[1],1)\n", + "\n", + "#Detune the drive laser by a relatively small amount, say 2 MHz.\n", + "wavelength_from_transition!(laser, ca, (\"S\", \"D\"), chamber)\n", + "detuning!(laser,2e6)\n", + "polarization!(laser, (x̂ - ẑ)/√2)\n", + "wavevector!(laser, (x̂ + ẑ)/√2)\n", + "intensity_from_pitime!(laser, 1e-7, ca, (\"S\", \"D\"), chamber); # Sets pi_time to 2 μs\n", + "\n", + "\n", + "\"\"\"\n", + "Let's look at the arguments for hamiltonian():\n", + "\n", + "hamiltonian(\n", + " chamber::Chamber;\n", + " rotatingframe::Union{RotatingFrame,String}=\"interaction\",\n", + " timescale::Real=1,\n", + " lamb_dicke_order::Union{Vector{Int}, Int}=1,\n", + " rwa_cutoff::Real=Inf,\n", + " displacement::String=\"truncated\",\n", + " time_dependent_eta::Bool=false\n", + ")\n", + "\n", + "Note that the only argument which must be supplied is chamber. The others all have default values, and the\n", + "default value of the rotatingframe argument is \"interaction\", a string. If this string or no argument is\n", + "supplied for the rotating frame, IonSim will automatically assume that you want to work in the interaction\n", + "picture. Let's see this in action:\n", + "\"\"\"\n", + "\n", + "h = hamiltonian(chamber, timescale=1e-6, rwa_cutoff=5e6, lamb_dicke_order=1)\n", + "S0 = ca[\"S\"] ⊗ modes(chamber)[1][1]\n", + "τ = 1\n", + "steps = 1000\n", + "tspan = 0:τ/steps:τ\n", + "ρi = dm(S0)\n", + "J = one(ρi)\n", + "γ = 1\n", + "\n", + "_, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h(t, ρ), [J], [J], [γ]))\n", + "\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"Off-resonant Rabi flops, old hamiltonians.jl\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "e5c48d72", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "And we see the dynamics we expect to see. Fiddling with the laser detuning will change the contrast and the \n", + "frequency of the oscillations, and we should see perfect contrast for Δ = 0.\n", + "\n", + "But how do we know that there is anything special about the interaction picture? Let's see what happens\n", + "when we construct a dummy RotatingFrame object which does nothing, and feed that to the hamiltonian() function.\n", + "\n", + "To construct a rotating frame, we need to define operators (using IonSim's convenience functions makes our lives\n", + "easier here). A rotating frame is constructed in general via\n", + "\n", + " U = Πⱼe^(-iϕⱼDⱼt)\n", + "\n", + "where j runs from 1 to the number of operators used to specify the frame, and Dⱼ is a diagonal operator.\n", + "ϕⱼ is specified by the user - in the example below, ϕ₁ is set to 0 so that U = 1 and we are not making any\n", + "rotating frame. This sort of \"hack\" is needed to see the lab frame hamiltonian because it is useless for any\n", + "computational purpose and IonSim does not have any motivation to keep track of it. However, it IS important\n", + "to take away from this that IonSim's RotatingFrame should be built with respect to the lab frame (not the\n", + "interaction picture), consistent with the idea that the interaction picture is just a specific choice of\n", + "rotating frame.\n", + "\"\"\"\n", + "\n", + "P₁₁ = IonSim.ionprojector(chamber,1)\n", + "P₂₂ = IonSim.ionprojector(chamber,2)\n", + "num = IonSim.number(chamber,1)\n", + "rf_lab = RotatingFrame(chamber,[(P₁₁,0.0)])\n", + "h1_lab = hamiltonian(chamber, rotatingframe=rf_lab, timescale=1e-6, rwa_cutoff=5e6, lamb_dicke_order=1)\n", + "_, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h1_lab(t, ρ), [J], [J], [γ]))\n", + "\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"Off-resonant Rabi flops, lab frame\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "ffba9a6c", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "┌ Warning: Interrupted. Larger maxiters is needed. If you are using an integrator for non-stiff ODEs or an automatic switching algorithm (the default), you may want to consider using a method for stiff equations. See the solver pages for more details (e.g. https://docs.sciml.ai/DiffEqDocs/stable/solvers/ode_solve/#Stiff-Problems).\n", + "└ @ SciMLBase /Users/justin/.julia/packages/SciMLBase/VdcHg/src/integrator_interface.jl:575\n" + ] + }, + { + "ename": "LoadError", + "evalue": "PyError ($(Expr(:escape, :(ccall(#= /Users/justin/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:43 =# @pysym(:PyObject_Call), PyPtr, (PyPtr, PyPtr, PyPtr), o, pyargsptr, kw))))) \nValueError('x and y must have same first dimension, but have shapes (1001,) and (1,)')\n File \"/Users/justin/.julia/conda/3/lib/python3.9/site-packages/matplotlib/axes/_axes.py\", line 1632, in plot\n lines = [*self._get_lines(*args, data=data, **kwargs)]\n File \"/Users/justin/.julia/conda/3/lib/python3.9/site-packages/matplotlib/axes/_base.py\", line 312, in __call__\n yield from self._plot_args(this, kwargs)\n File \"/Users/justin/.julia/conda/3/lib/python3.9/site-packages/matplotlib/axes/_base.py\", line 498, in _plot_args\n raise ValueError(f\"x and y must have same first dimension, but \"\n", + "output_type": "error", + "traceback": [ + "PyError ($(Expr(:escape, :(ccall(#= /Users/justin/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:43 =# @pysym(:PyObject_Call), PyPtr, (PyPtr, PyPtr, PyPtr), o, pyargsptr, kw))))) \nValueError('x and y must have same first dimension, but have shapes (1001,) and (1,)')\n File \"/Users/justin/.julia/conda/3/lib/python3.9/site-packages/matplotlib/axes/_axes.py\", line 1632, in plot\n lines = [*self._get_lines(*args, data=data, **kwargs)]\n File \"/Users/justin/.julia/conda/3/lib/python3.9/site-packages/matplotlib/axes/_base.py\", line 312, in __call__\n yield from self._plot_args(this, kwargs)\n File \"/Users/justin/.julia/conda/3/lib/python3.9/site-packages/matplotlib/axes/_base.py\", line 498, in _plot_args\n raise ValueError(f\"x and y must have same first dimension, but \"\n", + "", + "Stacktrace:", + " [1] pyerr_check", + " @ ~/.julia/packages/PyCall/7a7w0/src/exception.jl:62 [inlined]", + " [2] pyerr_check", + " @ ~/.julia/packages/PyCall/7a7w0/src/exception.jl:66 [inlined]", + " [3] _handle_error(msg::String)", + " @ PyCall ~/.julia/packages/PyCall/7a7w0/src/exception.jl:83", + " [4] macro expansion", + " @ ~/.julia/packages/PyCall/7a7w0/src/exception.jl:97 [inlined]", + " [5] #107", + " @ ~/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:43 [inlined]", + " [6] disable_sigint", + " @ ./c.jl:458 [inlined]", + " [7] __pycall!", + " @ ~/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:42 [inlined]", + " [8] _pycall!(ret::PyCall.PyObject, o::PyCall.PyObject, args::Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, Vector{Float64}}, nargs::Int64, kw::PyCall.PyObject)", + " @ PyCall ~/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:29", + " [9] _pycall!(ret::PyCall.PyObject, o::PyCall.PyObject, args::Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, Vector{Float64}}, kwargs::Base.Pairs{Symbol, String, Tuple{Symbol, Symbol}, NamedTuple{(:color, :label), Tuple{String, String}}})", + " @ PyCall ~/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:11", + " [10] (::PyCall.PyObject)(::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, ::Vararg{Any}; kwargs::Base.Pairs{Symbol, String, Tuple{Symbol, Symbol}, NamedTuple{(:color, :label), Tuple{String, String}}})", + " @ PyCall ~/.julia/packages/PyCall/7a7w0/src/pyfncall.jl:86", + " [11] top-level scope", + " @ In[46]:18", + " [12] eval", + " @ ./boot.jl:373 [inlined]", + " [13] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)", + " @ Base ./loading.jl:1196" + ] + } + ], + "source": [ + "\"\"\"\n", + "We see absolutely nothing happening! That is because the rwa_cutoff parameter tells the solver what frequencies\n", + "are too fast to bother trying to calculate - any terms in the hamiltonian oscillating faster than this are\n", + "set to zero, assumed to time average to zero over the timescale of interest. In the laboratory frame, the\n", + "transition terms oscillate at the laser frequency, which is far greater than 5 MHz, so we see no dynamics.\n", + "\n", + "But what if we just provide no rwa_cutoff? The default argument is ∞, so here goes nothing:\n", + "\"\"\"\n", + "\n", + "h1_lab = hamiltonian(chamber, rotatingframe=rf_lab, timescale=1e-6, lamb_dicke_order=1)\n", + "_, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h1_lab(t, ρ), [J], [J], [γ]))\n", + "\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"Off-resonant Rabi flops, lab frame\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "e44873a0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "As you probably will see, the solver fails to find a solution and throws an error in the face of such fast \n", + "oscillations. The interaction picture is IonSim's fastest and most convenient way to simulate near-resonant\n", + "dynamics.\n", + "\n", + "Of course, we could just manually construct the interaction picture as well.\n", + "\"\"\"\n", + "rf_int = RotatingFrame(chamber,[(P₁₁,energy(ca,\"S\",B=b)),(P₂₂,energy(ca,\"D\",B=b)),(num,1e6)])\n", + "h1_int = hamiltonian(chamber, rotatingframe=rf_int, timescale=1e-6, rwa_cutoff=5e6, lamb_dicke_order=1)\n", + "_, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h1_int(t, ρ), [J], [J], [γ]));\n", + "\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"Off-resonant Rabi flops, lab frame\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "394cefa8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "To drive our point home, let's look at one more on-resonant example with another rotating frame. This time,\n", + "we will choose\n", + "\n", + " U = e^(-iνP₂₂t)\n", + "\n", + "where we spin the excited state |2⟩ ≡ |D⟩ \"backwards\" at the laser frequency. This transformation is distinct\n", + "from the interaction picture, and for a two-level system is the transformation that totally eliminates time \n", + "dependence (hence the name rf_perfect below). We are so confident in this fact that we will set the rwa_cutoff\n", + "argument to 0, and still see the dynamics! This doesn't work for the interaction picture, unless the detuning\n", + "is zero. Try it!\n", + "\"\"\"\n", + "\n", + "c = 299792458\n", + "ν = c/wavelength(laser) + detuning(laser)\n", + "rf_perfect = RotatingFrame(chamber,[(P₂₂,ν)])\n", + "h1_perfect = hamiltonian(chamber, rotatingframe=rf_perfect, timescale=1e-6, rwa_cutoff=0, lamb_dicke_order=1)\n", + "_, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h1_perfect(t, ρ), [J], [J], [γ]));\n", + "\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"Off-resonant Rabi flops, lab frame\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);" + ] + }, + { + "cell_type": "markdown", + "id": "747d5e09", + "metadata": {}, + "source": [ + "# Off-resonant dynamics: Raman transitions" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "9693e225", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "Now we, consider a three-level (Λ) system comprised of two low-lying states |S⟩ and |D⟩, and a higher-energy \n", + "state |P⟩. |S⟩ ↔ |P⟩ and |P⟩ ↔ |D⟩ are dipole-allowed transitions, but |S⟩ ↔ |D⟩ is not. We may couple the two\n", + "low-lying states via two lasers, each of which couples one of the dipole-allowed transitions with a large\n", + "detuning. Each laser is far-detuned from the transition it drives, so that the population in the |P⟩ state is\n", + "nearly 0 for all time. We call this 'adiabatically eliminating' the |P⟩ state. The end result is a Rabi\n", + "oscillation between the |S⟩ and |D⟩ levels, whose contrast and frequency depends on the two-photon detuning, \n", + "\n", + " δ ≡ Δ₂ - Δ₁. \n", + "\n", + "This is known as a Raman process. The dynamics in the lab frame are at THz frequencies as usual, but in the \n", + "interaction picture, they are often still at hundreds of MHz.\n", + "\"\"\"\n", + "\n", + "ca = Ca40([(\"S1/2\", -1/2, \"S\"), (\"P3/2\",-1/2, \"P\"),(\"D5/2\", -1/2, \"D\")])\n", + "\n", + "#one motional mode\n", + "#νr = 4e6\n", + "#νa = 1e6\n", + "\n", + "\n", + "#two lasers\n", + "#set laser wavelength and power\n", + "Δ = 2π*300e6 #Absolute laser detuning is large compared to Ω₁, Ω₂\n", + "δ = 0#10e3 #two-photon detuning\n", + "Ω₁ = 10e6\n", + "Ω₂ = 10e6\n", + "l1 = Laser()\n", + "l2 = Laser()\n", + "\n", + "#configure trap\n", + "chain = LinearChain(\n", + " ions=[ca],\n", + " comfrequencies=(x=3e6,y=3e6,z=1e6), \n", + " selectedmodes=(;z=[1])\n", + " )\n", + "b = 0\n", + "chamber = Chamber(iontrap=chain, B=b, Bhat=ẑ, δB=0, lasers=[l1,l2])\n", + "wavelength_from_transition!(l1, ca, (\"S\", \"P\"), chamber)\n", + "wavelength_from_transition!(l2, ca, (\"D\", \"P\"), chamber)\n", + "detuning!(l1,Δ)\n", + "detuning!(l2,Δ+δ)\n", + "polarization!(l1, (x̂ - ẑ)/√2)\n", + "polarization!(l2, (x̂ - ẑ)/√2)\n", + "wavevector!(l1, (x̂ + ẑ)/√2)\n", + "wavevector!(l2, (x̂ + ẑ)/√2)\n", + "intensity_from_pitime!(l1, 1/(2*Ω₁), ca, (\"S\", \"P\"), chamber)\n", + "intensity_from_pitime!(l2, 1/(2*Ω₂), ca, (\"D\", \"P\"), chamber)\n", + "\n", + "axial = modes(chamber)[1]\n", + "modecutoff!(axial,1)\n", + "\n", + "# set initial state |S⟩ ⊗ |0⟩\n", + "ψi = ca[\"S\"]\n", + "ρi_ions = dm(ψi)\n", + "ρi_axial = dm(fockstate(axial, 0))\n", + "ρi = ρi_ions ⊗ ρi_axial\n", + "\n", + "J = one(dm(ψi)) ⊗ one(axial)\n", + "γ = 1\n", + "\n", + "Ω_eff = π*Ω₁*Ω₂/Δ\n", + "nflops = 2\n", + "τ = nflops/Ω_eff\n", + "steps = 1000\n", + "tspan = 0:τ/steps:τ\n", + "\n", + "#Let's go to the interaction picture!\n", + "\n", + "h_int = hamiltonian(chamber, rotatingframe=\"interaction\", rwa_cutoff=5e6, lamb_dicke_order=2)\n", + "_, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h_int(t, ρ), [J], [J], [γ]))\n", + "\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "plist = real(expect(ionprojector(chamber,\"P\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "nlist = real(expect(one(ρi_ions)⊗IonSim.number(axial),ρt))\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"One ion raman transition, interaction picture\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,plist,color=\"red\",label=\"|P⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "98558039", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 25.773821 seconds (185.90 M allocations: 10.562 GiB, 4.64% gc time, 15.03% compilation time)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject
)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\"\"\"\n", + "Now, we won't see any dynamics, because the lasers are far detuned from the transitions, so the interaction\n", + "picture isn't good enough - we would need an rwa cutoff of 300 MHz to see these dynamics!\n", + "But the two-photon detuning is small (the lasers are each detuned by the same amount), so maybe there is\n", + "another frame we could intelligently choose...?\n", + "\n", + "It turns out that there is a frame which we can choose to kill the time dependence. It can be worked out by\n", + "computing H̃ from the above, but with U having diagonal elements e^(-iϕⱼt), and computing which values of \n", + "ϕⱼ cause all time-varying terms in H̃ to cancel, or otherwise oscillate at a sum of atomic and optical \n", + "frequencies (to be thrown out in the RWA). This solution has a free parameter and so is not unique; the most \n", + "symmetric solution is the one chosen here.\n", + "\"\"\"\n", + "\n", + "P₁₁ = IonSim.ionprojector(chamber,1)\n", + "P₂₂ = IonSim.ionprojector(chamber,2)\n", + "P₃₃ = IonSim.ionprojector(chamber,3)\n", + "num = IonSim.number(chamber,1)\n", + "\n", + "ν1 = (c/wavelength(l1) + detuning(l1))\n", + "ν2 = (c/wavelength(l2) + detuning(l2))\n", + "\n", + "ϕ1 = (detuning(l2) - detuning(l1))/2\n", + "ϕ2 = ϕ1 + ν1\n", + "ϕ3 = ϕ2 - ν2\n", + "\n", + "rf_raman = RotatingFrame(chamber,[(P₁₁,ϕ1),(P₂₂,ϕ2),(P₃₃,ϕ3),(num,1e6)])\n", + "\n", + "Ω_eff = Ω₁*Ω₂/Δ\n", + "nflops = 2\n", + "τ = nflops/Ω_eff*1e6/π\n", + "steps = 1000\n", + "tspan = 0:τ/steps:τ\n", + "@time begin\n", + " h_raman = hamiltonian(chamber, rotatingframe = rf_raman, timescale=1e-6, rwa_cutoff=0, lamb_dicke_order=0)\n", + " _, ρt = timeevolution.master_dynamic(tspan, ρi, (t, ρ) -> (h_raman(t, ρ), [J], [J], [γ]))\n", + "end\n", + "slist = real(expect(ionprojector(chamber,\"S\"),ρt))\n", + "plist = real(expect(ionprojector(chamber,\"P\"),ρt))\n", + "dlist = real(expect(ionprojector(chamber,\"D\"),ρt))\n", + "nlist = real(expect(one(ρi_ions)⊗IonSim.number(axial),ρt))\n", + "\n", + "\n", + "fig, (ax1) = PyPlot.subplots(1)\n", + "fig.suptitle(\"One ion raman transition, rotating frame\")\n", + "ax1.plot(tspan,slist,color=\"blue\",label=\"|S⟩\")\n", + "ax1.plot(tspan,plist,color=\"red\",label=\"|P⟩\")\n", + "ax1.plot(tspan,dlist,color=\"green\",label=\"|D⟩\")\n", + "ax1.legend(loc=1);\n", + "\n", + "#= Look at the rwa cutoff, 0 once more! We have successfully chosen and implemented a rotating frame which\n", + "kills the time-dependence in the relevant terms.=#" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "64f308ba", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.7.3", + "language": "julia", + "name": "julia-1.7" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/IonSim.jl b/src/IonSim.jl index 80116e0..26a0267 100644 --- a/src/IonSim.jl +++ b/src/IonSim.jl @@ -40,6 +40,7 @@ include("lasers.jl") include("iontraps.jl") include("chambers.jl") include("operators.jl") +include("rotatingframes.jl") include("hamiltonians.jl") include("timeevolution.jl") include("species/_include_species.jl") diff --git a/src/hamiltonians.jl b/src/hamiltonians.jl index ae5132c..8d445d1 100644 --- a/src/hamiltonians.jl +++ b/src/hamiltonians.jl @@ -51,6 +51,7 @@ Constructs the Hamiltonian for `chamber` as a function of time. Return type is a """ function hamiltonian( chamber::Chamber; + rotatingframe::Union{RotatingFrame,String}="interaction", timescale::Real=1, lamb_dicke_order::Union{Vector{Int}, Int}=1, rwa_cutoff::Real=Inf, @@ -59,6 +60,7 @@ function hamiltonian( ) return hamiltonian( chamber, + rotatingframe, iontrap(chamber), timescale, lamb_dicke_order, @@ -74,8 +76,10 @@ end # At each time step, this function updates in-place the 2D array describing the full system # Hamiltonian. + function hamiltonian( chamber::Chamber, + rf::Union{RotatingFrame,String}, iontrap::LinearChain, timescale::Real, lamb_dicke_order::Union{Vector{Int}, Int}, @@ -85,6 +89,7 @@ function hamiltonian( ) b, indxs, cindxs = _setup_base_hamiltonian( chamber, + rf, timescale, lamb_dicke_order, rwa_cutoff, @@ -92,7 +97,16 @@ function hamiltonian( time_dependent_eta ) aui, gbi, gbs, bfunc, δνi, δνfuncs = _setup_fluctuation_hamiltonian(chamber, timescale) + interaction_picture = (typeof(rf)<:String) + if interaction_picture + @assert rf == "interaction" "argument rotatingframe must be the string \"interaction\" or be of type RotatingFrame" + else + Sdiag = rotating_eigenenergies(chamber,rf,timescale) + end S = SparseOperator(basis(chamber)) + + #could make rotating_eigenenergies return list and indices instead + #try to place this inside of an existing loop function f(t, ψ) # a two argument function is required in the QuantumOptics solvers @inbounds begin @simd for i in 1:length(indxs) @@ -116,6 +130,15 @@ function hamiltonian( end end end + + #Hit a new loop with an @inbounds begin\end and run a single loop over the nonzero diagonal elements + #Have a list of nonzero diagonal elements and a list of the indices corresponding to them + #only need to do this loop if we're not in the interaction picture + if !interaction_picture + for j in 1:length(basis(chamber)) + S.data[j,j] = Sdiag.data[j,j]#rotating_eigenenergies(chamber,rf,timescale).data[j,j]#S.data[j,j] + + end + end if length(gbi) == 0 && length(δνi) == 0 return S else @@ -139,6 +162,7 @@ function hamiltonian( end end end + return S end return f @@ -178,6 +202,7 @@ function does not keeps track of only one of these pairs. =# function _setup_base_hamiltonian( chamber, + rf, timescale, lamb_dicke_order, rwa_cutoff, @@ -185,9 +210,19 @@ function _setup_base_hamiltonian( time_dependent_eta ) rwa_cutoff *= timescale + + interaction_picture = (typeof(rf)<:String) + allmodes = reverse(modes(chamber)) L = length(allmodes) - νlist = Tuple([frequency(mode) for mode in allmodes]) + + if interaction_picture + νlist = Tuple([frequency(mode) for mode in allmodes]) + else + vibrationalϕlist = [rotatingphase(rf, create(chamber, L-(i-1))) for i in 1:L] + νlist = Tuple([vibrationalϕlist[i] for i in 1:L]) + end + mode_dims = [modecutoff(mode) + 1 for mode in allmodes] all_ions = reverse(ions(chamber)) @@ -195,7 +230,7 @@ function _setup_base_hamiltonian( ion_arrays = [spdiagm(0 => [true for _ in 1:shape(ion)[1]]) for ion in all_ions] ηm, Δm, Ωm = - _ηmatrix(chamber), _Δmatrix(chamber, timescale), _Ωmatrix(chamber, timescale) + _ηmatrix(chamber), _Δmatrix(chamber, rf, timescale), _Ωmatrix(chamber, timescale) lamb_dicke_order = _check_lamb_dicke_order(lamb_dicke_order, L) ld_array, rows, vals = _ld_array(mode_dims, lamb_dicke_order, νlist, timescale) if displacement == "truncated" && time_dependent_eta @@ -252,11 +287,13 @@ function _setup_base_hamiltonian( ri = rows[i] ri < j && continue cf = vals[i] + pflag = abs(Δ_2π + cf) > rwa_cutoff nflag = abs(Δ_2π - cf) > rwa_cutoff + (pflag && nflag) && continue rev_indxs = false - idxs = _inv_get_kron_indxs((rows[i], j), mode_dims) + idxs = inv_get_kron_indxs((rows[i], j), mode_dims) for l in 1:L (idxs[1][l] ≠ idxs[2][l] && typeof(ηnm[l]) <: Number) && @goto cl end @@ -404,6 +441,34 @@ function _setup_base_hamiltonian( return functions, repeated_indices, conj_repeated_indices end +function rotating_eigenenergies(chamber, rf, timescale) + S_diag = SparseOperator(basis(chamber)) + allmodes = (modes(chamber)) + allions = (ions(chamber)) + mode_dims = [modecutoff(mode) + 1 for mode in allmodes] + ion_dims = [shape(ion)[1] for ion in allions] + dims = mode_dims + for dim in ion_dims + push!(dims,dim) + end + for j in 1:length(basis(chamber)) + idxs = inv_get_kron_indxs((j,j), dims)[1] + Energy = 0 + + for (m,mode) in enumerate(allmodes) + Energy = Energy + frequency(mode)*(idxs[m]-1) + end + + for (n,ion) in enumerate(allions) + Energy = Energy + energy(ion,sublevels(ion)[idxs[n+length(allmodes)]],B=chamber.B) + end + S_diag.data[j,j] = timescale*(Energy - unitary(rf)[j]) + end + return S_diag +end + + + # δν(t) × aᵀa terms for Hamiltonian. This function returns an array of functions # δν_functions = [2π×ν.δν(t)×timescale for ν in modes]. It also returns an array of arrays # of arrays of indices, δν_indices, such that δν_indices[i][j] lists all diagonal elements @@ -517,23 +582,30 @@ end # respectively. For each row/column we have a vector of detunings from the laser frequency # for each ion transition. We need to separate this calculation from _Ωmatrix to implement # RWA easily. -function _Δmatrix(chamber, timescale) +function _Δmatrix(chamber, rf, timescale) all_ions = ions(chamber) all_lasers = lasers(chamber) (N, M) = length(all_ions), length(all_lasers) B = bfield(chamber) ∇B = bgradient(chamber) Δnmkj = Array{Vector}(undef, N, M) + interaction_picture = (typeof(rf)<:String) for n in 1:N, m in 1:M Btot = bfield(chamber, all_ions[n]) v = Vector{Float64}(undef, 0) for transition in subleveltransitions(all_ions[n]) - ωa = transitionfrequency(all_ions[n], transition, B=Btot) + #RF Edit: Instead of adjusting by the atomic frequency, adjust according to the rotating frame. + #ωa = transitionfrequency(all_ions[n], transition, B=Btot) + if interaction_picture + ϕ = transitionfrequency(all_ions[n], transition, B=Btot) + else + ϕ = rotatingphase(rf, n, transition) + end push!( v, 2π * timescale * - ((c / wavelength(all_lasers[m])) + detuning(all_lasers[m]) - ωa) + ((c / wavelength(all_lasers[m])) + detuning(all_lasers[m]) - ϕ) ) end Δnmkj[n, m] = v @@ -632,7 +704,7 @@ end # The inverse of _get_kron_indxs. If T = X₁ ⊗ X₂ ⊗ X₃ and X₁, X₂, X₃ are M×M, N×N and L×L # dimension matrices, then we should input dims=(M, N, L). -function _inv_get_kron_indxs(indxs, dims) +function inv_get_kron_indxs(indxs, dims) row, col = indxs N = length(dims) ret_rows = Array{Int64}(undef, N) @@ -703,4 +775,4 @@ function _ld_array(mode_dims, lamb_dicke_order, νlist, timescale) end length(a) == 1 ? ld_array = a[1] : ld_array = kron(a...) return ld_array, rowvals(ld_array), log.(nonzeros(ld_array)) -end +end; \ No newline at end of file diff --git a/src/operators.jl b/src/operators.jl index 7f99576..5b59992 100644 --- a/src/operators.jl +++ b/src/operators.jl @@ -24,18 +24,91 @@ returns the creation operator for `v` such that: `create(v) * v[i] = √(i+1) * """ create(v::VibrationalMode) = SparseOperator(v, diagm(-1 => sqrt.(1:(modecutoff(v))))) +""" + create(c::Chamber, mode_idx::Int64; onlymodes=false) +Returns the creation operator for the mode specified by mode_idx, tensored with the identity for all other modes. +If onlymodes=false, then the output is also tensored with the identity for all ions. +""" +function create(c::Chamber, mode_idx::Int64; onlymodes=false) + @assert (mode_idx <= length(modes(c))) & (mode_idx > 0) "Invalid mode index." + v = modes(c)[mode_idx] + if mode_idx == 1 + if length(modes(c)) > 1 + adag = create(v) ⊗ tensor([one(modes(c)[j]) for j in 2:length(modes(c))]...) + else + adag = create(v) + end + else + adag = one(modes(c)[1]) + for j in 2:length(modes(c)) + if j == mode_idx + adag = adag ⊗ create(v) + else + adag = adag ⊗ one(modes(c)[j]) + end + end + end + if onlymodes + return adag + end + return tensor([one(ion) for ion in ions(c)]...) ⊗ adag +end + + + + """ destroy(v::VibrationalMode) Returns the destruction operator for `v` such that: `destroy(v) * v[i] = √i * v[i-1]`. """ destroy(v::VibrationalMode) = create(v)' +""" + destroy(c::Chamber, mode_idx::Int64; onlymodes=false) +Returns the destruction operator for the mode specified by mode_idx, tensored with the identity for all other modes. +If onlymodes=false, then the output is also tensored with the identity for all ions. +""" +function destroy(c::Chamber, mode_idx::Int64; onlymodes=false) + return SparseOperator(create(c,mode_idx,onlymodes=onlymodes)') +end + """ number(v::VibrationalMode) Returns the number operator for `v` such that: `number(v) * v[i] = i * v[i]`. """ number(v::VibrationalMode) = SparseOperator(v, diagm(0 => 0:(modecutoff(v)))) +""" + number(c::Chamber, mode_idx::Int64; onlymodes=false) +Returns the number operator for the mode specified by mode_idx, tensored with the identity for all other modes. +If onlymodes=false, then the output is also tensored with the identity for all ions. +""" + +function number(c::Chamber, mode_idx::Int64; onlymodes=false) + @assert (mode_idx <= length(modes(c))) & (mode_idx > 0) "Invalid mode index." + v = modes(c)[mode_idx] + if mode_idx == 1 + if length(modes(c))>1 + num = number(v) ⊗ tensor([one(modes(c)[j]) for j in 2:length(modes(c))]...) + else + num = number(v) + end + else + num = one(modes(c)[1]) + for j in 2:length(modes(c)) + if j == mode_idx + num = num ⊗ number(v) + else + num = num ⊗ one(modes(c)[j]) + end + end + end + if onlymodes + return num + end + return SparseOperator(tensor([one(ion) for ion in ions(c)]...) ⊗ num) +end + """ displace(v::VibrationalMode, α::Number; method="truncated") Returns the displacement operator ``D(α)`` corresponding to `v`. @@ -68,6 +141,33 @@ function displace(v::VibrationalMode, α::Number; method="truncated") end end +""" + displace(c::Chamber, mode_idx::Int64, α::Number; method="truncated", onlymodes=false) +Returns the displacement operator for the mode specified by mode_idx, D(α), tensored with the identity for all other modes. +If onlymodes=false, then the output is also tensored with the identity for all ions. +""" +function displace(c::Chamber, mode_idx::Int64, α::Number; method="truncated", onlymodes=false) + @assert (mode_idx <= length(modes(c))) & (mode_idx > 0) "Invalid mode index." + v = modes(c)[mode_idx] + if mode_idx == 1 + dis = displace(v,α,method=method) ⊗ tensor([one(modes(c)[j]) for j in 2:length(modes(c))]...) + else + dis = one(modes(c)[1]) + for j in 2:length(modes(c)) + if j == mode_idx + dis = dis ⊗ displace(v,α,method=method) + else + dis = dis ⊗ one(modes(c)[j]) + end + end + end + if onlymodes + return dis + end + return SparseOperator(tensor([one(ion) for ion in ions(c)]...) ⊗ dis) +end + + """ thermalstate(v::VibrationalMode, n̄::Real; method="truncated") Returns a thermal density matrix with ``⟨a^†a⟩ ≈ n̄``. Note: approximate because we are @@ -183,6 +283,32 @@ sigma(ion::Ion, ψ1::T, ψ2::T) where {T <: Union{Tuple{String, Real}, String, I sparse(projector(ion[ψ1], dagger(ion[ψ2]))) sigma(ion::Ion, ψ1::Union{Tuple{String, Real}, String, Int}) = sigma(ion, ψ1, ψ1) +""" + sigma(c::Chamber, ion_idx::Int64, ψ1::sublevel, ψ2::sublevel, onlyions=false) +Returns the transition operator for the ion specified by ion_idx undergoing the transition ψ2 --> ψ1, tensored with the identity for all other ions. +If onlyions=false, then the output is also tensored with the identity for all modes. +""" +function sigma(c::Chamber, ion_idx::Int64, ψ1::T, ψ2::T, onlyions=false) where {T <: Union{Tuple{String, Real}, String, Int}} + @assert (ion_idx <= length(ions(c))) & (ion_idx > 0) "Invalid ion index." + ion = ions(c)[ion_idx] + if ion_idx == 1 + sig = sigma(ion,ψ1,ψ2) ⊗ tensor([one(ions(c)[j]) for j in 2:length(ions(c))]...) + else + sig = one(ions(c)[1]) + for j in 2:length(ions(c)) + if j == ion_idx + sig = sig ⊗ sigma(ion,ψ1,ψ2) + else + sig = sig ⊗ one(ions(c)[j]) + end + end + end + if onlyions + return SparseOperator(sig) + end + return SparseOperator(sig ⊗ tensor([one(mode) for mode in modes(c)]...)) +end + """ ionprojector(obj, sublevels...; only_ions=false) diff --git a/test/runtests.jl b/test/runtests.jl index f6710bb..ce00c50 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -8,3 +8,4 @@ include("test_ion_traps.jl") include("test_chambers.jl") # include("test_hamiltonians.jl") include("test_dynamics.jl") +include("test_rotatingframes.jl")