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arXiv:2102.11140 · Physical Review Letters

Non-Markovian Steady States of a Driven Two-Level System

Andreas Ask, Göran Johansson

Published Feb 23, 2022• 0 citations
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Abstract

We show that an open quantum system in a non-Markovian environment can reach steady states that it cannot reach in a Markovian environment. As these steady states are unique for the non-Markovian regime, they could offer a simple way of detecting non-Markovianity, as no information about the system's transient dynamics is necessary. In particular, we study a driven two-level system (TLS) in a semi-infinite waveguide. Once the waveguide has been traced out, the TLS sees an environment with a distinct memory time. The memory time enters the equations as a time delay that can be varied to compare a Markovian to a non-Markovian environment. We find that some non-Markovian states show exotic behaviors such as population inversion and steady-state coherence beyond 1/sqrt[8], neither of which is possible for a driven TLS in the Markovian regime, where the time delay is neglected. Additionally, we show how the coherence of quantum interference is affected by time delays in a driven system by extracting the effective Purcell-modified decay rate of a TLS in front of a mirror.

DOI
10.1103/physrevlett.128.083603

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We show that an open quantum system in a non-Markovian environment can reach steady states that it cannot reach in a Markovian environment. As these steady states are unique for the non-Markovian regime, they could offer a simple way of detecting non-Markovianity, as no information about the system's transient dynamics is necessary. In particular, we study a driven two-level system (TLS) in a semi-infinite waveguide. Once the waveguide has been traced out, the TLS sees an environment with a distinct memory time. The memory time enters the equations as a time delay that can be varied to compare a Markovian to a non-Markovian environment. We find that some non-Markovian states show exotic behaviors such as population inversion and steady-state coherence beyond 1/sqrt[8], neither of which is possible for a driven TLS in the Markovian regime, where the time delay is neglected. Additionally, we show how the coherence of quantum interference is affected by time delays in a driven system by extracting the effective Purcell-modified decay rate of a TLS in front of a mirror.
We show that an open quantum system in a non-Markovian environment can reach steady states that it cannot reach in a Markovian environment. As these steady states are unique for the non-Markovian regime, they could offer a simple way of detecting non-Markovianity, as no information about the system's transient dynamics is necessary. In particular, we study a driven two-level system (TLS) in a semi-infinite waveguide. Once the waveguide has been traced out, the TLS sees an environment with a distinct memory time. The memory time enters the equations as a time delay that can be varied to compare a Markovian to a non-Markovian environment. We find that some non-Markovian states show exotic behaviors such as population inversion and steady-state coherence beyond 1/8, neither of which is possible for a driven TLS in the Markovian regime, where the time delay is neglected. Additionally, we show how the coherence of quantum interference is affected by time delays in a driven system by extracting the effective Purcell-modified decay rate of a TLS in front of a mirror.
The non-Markovian effects of open quantum systems subjected to external environments are deemed to be valuable resources in quantum optics and quantum information processing. In this work, we construct the model Hamiltonian of three-level giant atom with multiple coupling points in the semi-infinite photonic waveguide via complex coupling coefficients and investigate the non-Markovian dynamics of the three-level giant atom driven by a classical laser field. In the non-Markovian regime, the traveling time of a photon between different coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. We derive the analytical expressions for the probability amplitudes of the driven three-level giant atom by solving a set of delay differential equations and obtain two independent conditions of bound states' formation that can inhibit the dissipation. We find two different types of bound states (including the static bound states and the periodic equal-amplitude oscillating bound states) and discuss the physical origins of the bound states' formation. Moreover, we discuss the case of the driven three-level giant atom interacting with the infinite photonic waveguide, where there is only one purely imaginary solution (i.e., only one bound-state condition exists) for its complex frequency (coming from the absence of mirror at one end of the waveguide) compared to that of a driven three-level giant atom coupling with a semi-infinite photonic waveguide. With this, we also find two different types of bound states, including the static bound state and the periodic equal-amplitude oscillating bound states. We study the influences of the phase in the coupling strength on the bound states in semi-infinite and infinite photonic waveguides. The presented protocol might open a way to better understand exactly the non-Markovian dynamics of driven multilevel giant atoms interacting with semi-infinite (or infinite) photonic waveguides.
We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.
We study the decoherence dynamics of a superconducting qubit coupled to a quantum two-level system (TLS) in addition to its weak coupling to a background environment [1]. We identify two weak-coupling regimes, which differ by the relation between qubit and TLS decoherence times, and a strong coupling regime. We find expressions for the qubit decoherence rates in the weak-coupling regimes. For a weakly coupled and strongly dissipative TLS we find that the qubit dynamics is markovian, whereas for a weakly dissipative TLS the qubit dynamics shows non-markovian behavior. In the strong-coupling regime we study the driven qubit dynamics and we analyze the differences from standard Rabi-oscillations due to the coupling to the quantum TLS [2]. In doing so we identify signatures in the qubit dynamics that can be used to characterize the TLS. We also investigate the possibility of using environmental TLSs with long coherence times for quantum information processing [3]. By using the Josephson junction as a bus and the TLSs in the environment as qubits, we demonstrate that initialization, a universal set of quantum gates, and read-out of the TLSs can be implemented, even though the TLSs themselves cannot be directly accessed.
We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM mn ) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity N 1 can be found as the atom–mirror distance is large enough, however, the asymptotic value of N 2 of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that N 1 is a constant, and the analytical expression for N 2 is related to the parameters associated with the modes, which is related to the interference of the two modes.
The reduced description of the quantum dynamic processes in the condensed phase environment leads to the equation of motion with a memory kernel. Such a memory effect, termed non-Markovianity, presents more complex dynamics compared to its memoryless or Markovian counterpart, and many chemical systems have been demonstrated through numerical simulations to exhibit non-Markovian quantum dynamics. Explicitly how the memory impacts the dynamic process remains largely unexplored. In this work, we focus on ways to separate the non-Markovian contributions from the dynamics and study the non-Markovian effects. Specifically, we developed a rigorous procedure for mapping the exact non-Markovian quantum propagator to the Lindblad form. Consequently, it allows us to extract the negative decay rate from the Lindbladian that is the signature of the non-Markovianity. By including or excluding the negative rate in the time evolution, we can decisively pinpoint the influence of non-Markovianity on the system's properties such as coherence, entanglement, and equilibrium state distribution. The understanding of such memory effects on the dynamic process suggests the possibility of leveraging non-Markovianity for quantum control.