Adiabatic state preparation and thermalization of simulated phase noise in a Rydberg spin Hamiltonian

Abstract

Laser phase noise is one of the main sources of decoherence in driven Rydberg systems with neutral atoms in tweezer arrays. While the effect of phase noise in the regimes of isolated qubits and few-qubit gate protocols has been studied extensively, there are open questions about the effects of this noise on many-body systems. In many scenarios, the effects of noise cannot simply be described by an increase in the energy or temperature of the system, leading to non-trivial changes in the state and relevant correlations. In this work, we use stochastic sampling to simulate laser phase noise based on experimentally relevant spectral densities. We explore the impact of this noise on adiabatic state preparation in a one-dimensional system, discussing the interplay between heating and interactions during dynamics. We find that for certain adiabatic processes, the noise can be seen to approximately thermalize in terms of its effects on relevant correlation functions.

Figures (12)

• Figure 1: Laser parameter space plot and ground state energy gap surface plot for the Rydberg Hamiltonian seen in Eq. \ref{['Ryd Hamil']} for a chain of $N=11$ atoms. (a) A schematic diagram showing crystalline ordering of ground state (blue) and Rydberg excited (red) atoms for initial and target many-body state of adiabatic state preparation. (b) Total fraction of excited Rydberg atoms $N_R/N$ in the ground state plotted against laser parameters $\Omega$ and$\delta$, from no excitations (blue), to half filled (white), to fully excited (red). The path for the diabatic state preparation studied is provided with color gradient from white to green tracking ground state energy gap. (c) Surface plot of the ground state energy gap in the region of positive $\delta/V_{dd}$, with the path of adiabatic state preparation in this region highlighted in red.
• Figure 2: (a) Laser parameters for three step adiabatic state preparation of a $Z_2$ ordered crystalline state for a 11 atom Rydberg chain. Rabi frequency $\Omega$ (red) is tuned linearly in step 1,3 for periods $T_1$, $T_3$, while detuning $\delta$ (green) is tuned linearly only in step 2 for a period of $T_2$. (b) Concurrent fidelity measured as the wavefunction overlap between the ground state $|\psi_{gr}\rangle$ of the instantaneous Hamiltonian $\hat{H}_{R}(t)$ and the evolved state $|\psi\rangle$. (c) Energy gap $\Delta E_{gr}$ between the instantaneous ground state and the first excited state.
• Figure 3: Realistic noise power spectrum used to generate independent phase noise time realizations implemented in adiabatic time evolution. (a) The phase noise spectrum $S_\phi$ (green) which has been converted from a frequency spectrum $S_\nu$ (red) used in noise generation. The relevant conversion equation is $S_\phi=\nu^2S_\nu$. (b) Three independent noise realizations generated using $S_\phi$ (see Appendix \ref{['NoiseGEN']}) provided in units of $tV_{dd}$ where $V_{dd}/2\pi=10$MHz. The averaged noise behavior after 100 independently generated noise realizations is shown in blue.
• Figure 4: Final fidelity of prepared state $|\psi(T)\rangle$ with the instantaneous ground state $|\psi_{gr}(T)\rangle$ at the end of the ramp, and final energy $E_T$ relative to the ground state energy $E_{gr}=\langle\psi_{gr}| H_R|\psi_{gr}\rangle$ after simulations using different evolution times $T_2$ for stage 2 (a,b), and $T_3$ for stage 3 (c,d) in the adiabatic state preparation described in Figure \ref{['fig:Ryd Adiab Sketch']} with added laser phase noise. Colored lines show results for noisy state preparation with a variety of system sizes, while the black line provides a reference for 11 sites and no added noise. Optimal values of $T_2$ resulting in highest fidelity for a given $N$ are highlighted in larger magenta circles in (a), with their final states used for $T_3$ analysis in (c,d). Each data point has error bars showing associated standard error after averaging over 100 preparations with unique laser phase noise signals generated from the same power spectrum in Figure \ref{['fig:My PSD']}. These results have been calculated using tensor network simulations using the iTensor package in Julia itensor, with time evolution achieved using the TDVP algorithm with a maximum bond dimension of 100.
• Figure 5: Final fidelities of the prepared state $|\psi(T_3)\rangle$ with $Z_2$ ordered ground state $|\psi_{gr}(T_3)\rangle$ for the adiabatic state preparation described in Figure \ref{['fig:Ryd Adiab Sketch']} with optimal evolution times for stage 2 ($T_2V_{dd}=82$) and stage 3 ($T_3V_{dd}=83$), and two varying parameters. (a) Final fidelity for different linear scalings of magnitude $m$ are applied directly to phase noise $\phi(t)\rightarrow m\phi(t)$. (b) Final fidelities for different values of $V_{dd}/2\pi$ ranging from $0.1-10$MHz. Colored lines show results for different system sizes. Error bars show standard error after averaging 100 preparations with unique laser phase noise signals. These results have been calculated using tensor network simulations using the iTensors package in Julia itensor, with time evolution achieved using the TDVP algorithm with a maximum bond dimension of 100.