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<p id="main-header-text">A lightweight Julia package for simulating the dynamics of a configuration of trapped ions interacting with laser light. </p>
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<p>IonSim leverages <a href="https://qojulia.org/" target="_blank">QuantumOptics.jl</a> to deliver a performant, quantitatively faithful tool for simulating fundamental interactions in trapped ion experiments. Several ion species and
trap configurations are implemented and everything is written in the language of experimentalists (ions and lasers, not qubits and gates).</p>
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<td class="align-middle left-td"><span class="index-code-block index-code-block-left swiper-no-swiping"><pre>
<code class="no-line-numbers">
using IonSim
using QuantumOptics
# Construct the system
C = Ca40([("S1/2", -1/2), ("D5/2", -1/2)])
set_sublevel_alias!(C, Dict("S" => ("S1/2", -1/2),
"D" => ("D5/2", -1/2)))
L1 = Laser(ϕ=π); L2 = Laser() # note the π-phase between L1/L2
chain = LinearChain(ions=[C, C], com_frequencies=(x=3e6, y=3e6, z=2.5e5),
vibrational_modes=(;z=[1]))
T = Trap(configuration=chain, B=6e-4, Bhat=(x̂ + ẑ)/√2,
lasers=[L1, L2])
mode = T.configuration.vibrational_modes.z[1]
# Set the laser parameters
ϵ = 10e3
d = 350 # correct for single-photon coupling to sidebands
L1.λ = transitionwavelength(C, ("S", "D"), T)
L2.λ = transitionwavelength(C, ("S", "D"), T)
L1.Δ = mode.ν + ϵ - d
L2.Δ = -mode.ν - ϵ + d
L1.k = L2.k = ẑ
L1.ϵ = L2.ϵ = x̂
# set 'resonance' condition: ηΩ = 1/2ϵ
η = abs(get_η(mode, L1, C))
E = Efield_from_pi_time!(η/ϵ, T, 1, 1, ("S", "D"))(0)
Ω = t -> t < 20 ? E * sin(2π * t / 80)^2 : E # ampl. ramp
L1.E = L2.E = Ω
# Build Hamiltonian
h = hamiltonian(T, lamb_dicke_order=1, rwa_cutoff=Inf)
# Solve
t, sol = timeevolution.schroedinger_dynamic(0:.1:220, C["S"] ⊗ C["S"] ⊗ mode[0], h);
</code></pre></span>
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<code class="no-line-numbers">
import PyPlot
const plt = PyPlot
SS = expect(ionprojector(T, "S", "S"), sol)
DD = expect(ionprojector(T, "D", "D"), sol)
SD = expect(ionprojector(T, "S", "D"), sol)
DS = expect(ionprojector(T, "D", "S"), sol)
plt.plot(t, SS, label="SS")
plt.plot(t, DD, label="DD")
plt.plot(t, SD, label="SD")
plt.plot(t, DS, label="DS")
plt.plot(t, @.(Ω(t) / 2E), ls="--", label="scaled ramp")
plt.legend(loc=1)
plt.xlim(t[1], t[end])
plt.ylim(0, 1)
plt.xlabel("Time (μs)")
plt.grid()
</code></pre></span><img class="slide-plot" src="assets/img/msplot_tight.png" style="text-align: center; display:inline;"></span>
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<td class="align-middle left-td"><span class="index-code-block index-code-block-left swiper-no-swiping"><pre>
<code class="no-line-numbers">
using IonSim
using QuantumOptics
# Construct the system
C = Ca40([("S1/2", -1/2), ("D5/2", -1/2)])
set_sublevel_alias!(C, Dict("S" => ("S1/2", -1/2),
"D" => ("D5/2", -1/2)))
L = Laser()
chain = LinearChain(
ions=[C], com_frequencies=(x=3e6, y=3e6, z=1e6),
vibrational_modes=(;z=[1])
)
T = Trap(configuration=chain, B=4e-4, Bhat=ẑ, lasers=[L])
# Set the laser parameters
L.k = (x̂ + ẑ)/√2
L.ϵ = (x̂ - ẑ)/√2
L.λ = transitionwavelength(C, ("S", "D"), T)
Efield_from_pi_time!(2e-6, T, 1, 1, ("S", "D"))
# Set the vibrational mode Hilbert space dimension
mode = T.configuration.vibrational_modes.z[1]
mode.N = 100
# Construct initial state
ρi_ion = dm(C["S"])
ρi_mode = thermalstate(mode, 10) # thermal state n̄=10
ρi = ρi_ion ⊗ ρi_mode
# Construct the hamiltonian
h = hamiltonian(T, timescale=1e-6)
# Solve the system
tout, sol = timeevolution.schroedinger_dynamic(0:.1:50, ρi, h);
</code></pre></span>
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<code class="no-line-numbers">
import PyPlot
const plt = PyPlot
plt.plot(
tout, expect(ionprojector(T, "D"), sol),
label="Excited State Population"
)
plt.xlim(tout[1], tout[end])
plt.ylim(0, 1)
plt.grid()
plt.xlabel("Time (μs)")
plt.legend(loc=1)
</code></pre></span><img class="slide-plot" src="assets/img/rabi-flop.png" style="text-align: center; display:inline;"></span>
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<code class="no-line-numbers">
using IonSim
using QuantumOptics
# Construct the system
C = Ca40([("S1/2", -1/2), ("D5/2", -1/2)])
set_sublevel_alias!(C, Dict("S" => ("S1/2", -1/2),
"D" => ("D5/2", -1/2)))
L = Laser()
chain = LinearChain(
ions=[C], com_frequencies=(x=3e6, y=3e6, z=1e6),
vibrational_modes=(;z=[1])
)
T = Trap(configuration=chain, B=2.9e-4, Bhat=ẑ, lasers=[L])
# Set the laser parameters
L.k = (x̂ + ẑ)/√2
L.ϵ = (x̂ - ẑ)/√2
L.λ = transitionwavelength(C, ("S", "D"), T)
# Set pi_time to 4 μs
E = Efield_from_pi_time(4e-6, T, 1, 1, ("S", "D"))
# We'll linearly sweep through the laser's frequency over
# [-125, +125] kHz (detuned from the carrier transition) in a time Tp
Tp = 250
Δϕ = Tp * 1e-3
L.ϕ = t -> 2π * (-Δϕ/2 + (Δϕ / Tp) * t) * t
# And also smoothly turn on and off the laser's electric field strength
Ω = t -> E * sin(π * t/Tp)^2
L.E = Ω
# Build Hamiltonian
h = hamiltonian(T, rwa_cutoff=Inf, lamb_dicke_order=1)
# Solve system
mode = T.configuration.vibrational_modes.z[1]
tout, sol = timeevolution.schroedinger_dynamic(0:.1:Tp, C["S"] ⊗ mode[0], h);
</code></pre></span>
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<code class="no-line-numbers">
import PyPlot
const plt = PyPlot
plt.plot(tout, expect(ionprojector(T, "D"), sol),
lw=3, color="C3", label="excited state population")
plt.plot(tout, @.(L.E(tout) / 2E),
ls="--", label="scaled amplitude profile")
plt.plot(tout, @.(L.ϕ(tout) / (2π * Δϕ * tout)),
ls="--", label="scaled frequency profile")
plt.xlim(tout[1], tout[end])
plt.legend(loc=4)
plt.grid()
plt.xlabel("Time (μs)")
</code></pre></span><img class="slide-plot" src="assets/img/rap.png" style="text-align: center; display:inline;"></span>
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<li><span class="bullet-title-text"><strong>Fast:</strong></span><strong> </strong>runtimes comparable to <a href="http://qutip.org/" target="_blank">QuTiP</a> (Cython)</li>
<li><span class="bullet-title-text"><strong>Intuitive:</strong></span><strong> </strong>you set up your simulation the same way that you set up your experiments</li>
<li><span class="bullet-title-text"><strong>Flexible:</strong></span><strong> </strong>full control over RWA cutoff frequencies, Lamb-Dicke order approximations, Hilbert space truncation and methods</li>
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<p>IonSim is maintained by <a href="https://ions.berkeley.edu" target="_blank">Hartmut Haeffner's trapped ion group</a> at UC Berkeley.</p>
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