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arXiv:2407.05171

Entanglement marker for lifetime of time crystal in transmon-modulated open Dicke model

Tanaya Ray, Shuva Mondal, Ujjwal Sen

Published Jul 6, 2024• 0 citations
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Abstract

We investigate the discrete time crystal (DTC) phase in a qubit ensemble, periodically driven by its interaction with either a photon or a transmon field, which is prone to dissipative leakage. We find this DTC to be robust against changes in detuning and anharmonicity of the field mode. Additionally, we study the system in the semiclassical limit, where mean-field approximations are valid, and demonstrate the utility of a suitable semiclassical Hamiltonian for this purpose. Intriguingly, we observe that the system exhibits a transient DTC even with only two qubits. We examine the dynamics of bipartite entanglement between the qubits and the field. Our findings show that the entanglement saturates to a steady value early in the dynamics, following a sudden peak. We find a strong positive correlation between this long-term entanglement value and the lifetime of the transient DTC, in a wide range of the parameter regime where the field is due to a lossy photon or a lossy transmon mode, with small detuning.

DOI
10.48550/arxiv.2407.05171

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We investigate the discrete time crystal (DTC) phase in a qubit ensemble, periodically driven by its interaction with either a photon or a transmon field, which is prone to dissipative leakage. We find this DTC to be robust against changes in detuning and anharmonicity of the field mode. Additionally, we study the system in the semiclassical limit, where mean-field approximations are valid, and demonstrate the utility of a suitable semiclassical Hamiltonian for this purpose. Intriguingly, we observe that the system exhibits a transient DTC even with only two qubits. We examine the dynamics of bipartite entanglement between the qubits and the field. Our findings show that the entanglement saturates to a steady value early in the dynamics, following a sudden peak. We find a strong positive correlation between this long-term entanglement value and the lifetime of the transient DTC, in a wide range of the parameter regime where the field is due to a lossy photon or a lossy transmon mode, with small detuning.
We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation. In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in presence of Jaynes-Cummings-like dissipation, we show that non-Markovian regime can be highly beneficial for stabilizing DTCs over a wide range of parameter values. This may be attributed to periodically varying dissipation rates even at long times in the case of non-Markovian dynamics. Further the Markovian and non-Markovian regimes show sharp distinctions for intermediate strengths of the dissipator coefficient, with a time-independent steady state in the Markovian regime being replaced by varied dynamical phases, including DTC order, in the non-Markovian regime. We also verify the robustness of the DTC phase in the non-Markovian regime by introducing errors both in the Hamiltonian as well as in the dissipation. Our study shows the possibility of using DTC as a probe for non-Markovian dynamics in periodically modulated open quantum systems, at long times.
We investigate the dynamics of coupled discrete time crystals (DTCs) in the coupled Dicke model or Dicke dimer (DD) with dissipation. By numerically simulating the mean-field dynamics of the system, we show that coupling two DTCs decreases their oscillation amplitude following a transient relaxation period. For sufficiently strong coupling, the coupled DTCs become unstable, resulting in the system relaxing towards the normal phase (NP). We demonstrate that the relaxation time diverges near the critical coupling strength, suggesting a continuous phase transition. Using the truncated Wigner approximation (TWA), we explore how the dynamics are affected by the introduction of quantum fluctuations. We also consider a scenario in which an NP is briefly coupled to a DTC, seeding the NP to transform into a DTC that is either synchronized or anti-synchronized relative to the DTC. We investigate the robustness of this phenomenon in the presence of noise. Using these results, we propose a scheme to perform NAND and NOR operations with three DTCs by sequentially coupling the input and output sites. We identify the parameter regimes in which the logic gate architecture remains valid, and investigate how the protocol is affected by the presence of quantum fluctuations.
It has been shown that Discrete Time Crystal (DTC) behavior may arise in the periodically driven, open Dicke model in the thermodynamic limit (N→∞N \rightarrow \inftyN→∞). In this work, we demonstrate that finite NNN non-mean-field fluctuations in this model can lead to decay rates and amplitudes of transient DTCs that display a non-trivial non-monotonic behavior with an increasing number of atoms. We show that the second-order cumulant expansion fails to capture the finite-size dynamics, while a stochastic version of the Truncated Wigner Approximation (TWA) is remarkably accurate, particularly in the large atom ensemble limit. Using the TWA and the Monte Carlo Wave Function (MCWF) approach, we identify three distinct dynamical regimes of transient DTC behavior in the finite-size Dicke model. We outline the mechanism behind the non-monotonic finite size dynamical decay of DTC order and discuss the implications for experiments performed on finite-sized atomic assemblies.
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)NATUAS0028-083610.1038/nature21426]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.
Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.
Discrete time crystals (DTC) have emerged as a significant phase of matter for out-of-equilibrium many-body systems. In this work, we study how random long-range interactions contribute to the stability of the DTC phase. Generally, a stable DTC phase is believed to be realized in disordered systems with short-range interactions. Here, we explore a periodically driven quantum Sherrington-Kirkpatrick (SK) model of Ising spin-glass in which all spins are coupled to each other randomly. We investigate the possibilities of the DTC phase in the SK model within three different driving protocols and found that the quantum SK model exhibits a robust DTC phase, although systems with uniform long-range interactions can exhibit only prethermal DTC phase. Further, we demonstrate that disorder in the local XYXYXY term or transverse field is crucial for stabilizing a broad DTC phase, despite random couplings in the SK model. Our analysis shows that the stability of the DTC phase is determined by the non-ergodic nature of the Floquet eigenstates.