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arXiv:1802.08283 · Physical Review Letters

Steady-State Coherences by Composite System-Bath Interactions

Giacomo Guarnieri, Michal Kolář, Radim Filip

Published Aug 15, 2018• 93 citations
arXivHTMLPDF

Abstract

We identify sufficient conditions on the structure of the interaction Hamiltonian between a two-level quantum system and a thermal bath that, without any external drive or coherent measurement, guarantee the generation of steady-state coherences (SSC). The SSC obtained this way, remarkably, turn out to be independent of the initial state of the system, which could therefore be taken as initially incoherent. We characterize in detail this phenomenon, first analytically in the weak coupling regime for two paradigmatic models, and then numerically in more complex systems without any assumption on the coupling strength. In all of these cases, we find that SSC become increasingly significant as the bath is cooled down. These results can be directly verified in many experimental platforms.

DOI
10.1103/physrevlett.121.070401

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Comment on "Steady-State Coherences by Composite System-Bath Interactions"

Marco Cattaneo, Gonzalo Manzano

In a recent Letter, Guarnieri et al. [1] reported on the possibility of generating steady-state coherence (SSC) in the energy basis of a two-level system by the sole action of a single thermal bath also for weak system-bath coupling and due to a composite form of this interaction. The results are based on a time-local Bloch-Redfield master equation without secular approximation and the associated set of Bloch equations, all derived in the Supplemental Material (SM) of Ref. [1]. We comment that the results reported by the authors present both technical flaws and conceptual limitations that substantially impact some of their main conclusions. Our objections mainly concern (a) technical errors in the calculation of SSC (Eqs.(2)-(4) in [1]) and (b) negativity issues associated with the weak-coupling master equation employed by the authors.

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We identify sufficient conditions on the structure of the interaction Hamiltonian between a two-level quantum system and a thermal bath that, without any external drive or coherent measurement, guarantee the generation of steady-state coherences (SSC). The SSC obtained this way, remarkably, turn out to be independent of the initial state of the system, which could therefore be taken as initially incoherent. We characterize in detail this phenomenon, first analytically in the weak coupling regime for two paradigmatic models, and then numerically in more complex systems without any assumption on the coupling strength. In all of these cases, we find that SSC become increasingly significant as the bath is cooled down. These results can be directly verified in many experimental platforms.
The appearance of steady-state coherence (SSC) from system-bath interactions proves that quantum effects can appear without an external drive. Such SSC could become a resource to demonstrate a quantum advantage in the applications. We predict the generation of SSC if the target system repeatedly interacts with independent and noncorrelated bath elements. To describe their behavior, we use the collision model approach of system-bath interactions, where the system interacts with one bath element (initially in an incoherent state) at a time, asymptotically (in the fast-collision regime) mimicking a macroscopic Markovian bath coupled to the target system. Therefore, the SSC qualitatively appears to be the same as if the continuous Markovian bath were used. We confirm that the presence of composite system-bath interactions under the rotating-wave approximation is the necessary condition for the generation of SSC using thermal resources in collision models. Remarkably, we show that SSC substantially increases if the target system interacts collectively with more than one bath element at a time. A few bath elements collectively interacting with the target system is sufficient to increase SSC at nonzero temperatures at the cost of a tolerable lowering of the final state purity. From the thermodynamic perspective, the SSC generation in our collision models is inevitably linked to a nonzero power input (and thus heat dissipated to the bath) necessary to reach the steady state, although such energetic cost can be lower compared to cases relying on SSC nongenerating interactions.
In a recent Letter, Guarnieri et al. [1] reported on the possibility of generating steady-state coherence (SSC) in the energy basis of a two-level system by the sole action of a single thermal bath also for weak system-bath coupling and due to a composite form of this interaction. The results are based on a time-local Bloch-Redfield master equation without secular approximation and the associated set of Bloch equations, all derived in the Supplemental Material (SM) of Ref. [1]. We comment that the results reported by the authors present both technical flaws and conceptual limitations that substantially impact some of their main conclusions. Our objections mainly concern (a) technical errors in the calculation of SSC (Eqs.(2)-(4) in [1]) and (b) negativity issues associated with the weak-coupling master equation employed by the authors.
We study a two-level system with an additional tunneling effect, where the general interaction with an Ohmic-class spectrum can be controlled by adjusting the coupling angle. We outline the derivation of the time-local microscopic non-Markovian master equation after renormalizing the eigenstates in the two-level system, hence removing the restriction of weak tunneling coupling. Further, two quantum coherence measures are exploited to analyze steady-state coherences (SSC). We identify that under strong tunneling effects, a specific coupling angle enables SSC generation that is both independent of the Ohmic-like spectral density and capable of reaching substantial magnitudes. Moreover, in the vicinity of this critical angle, SSC exhibits an opposite dependence on the Ohmic parameter in different regions. In addition, we examine the impact of Ohmic parameters and environmental temperature on SSC, demonstrating that optimizing these factors provides an effective strategy to maximize SSC.
Abstract Quantum superposition of energy eigenstates can appear autonomously in a single quantum two-level system coupled to a low-temperature thermal bath, if such coupling has a proper composite nature. We propose here a principally different and more feasible approach employing engineered interactions between two-level systems being thermalized into a global Gibbs state by weakly coupled thermal bath at temperature T. Therefore, in such case quantum coherence appears by a different mechanism, whereas the system-bath coupling does not have to be engineered. We demonstrate such autonomous coherence generation reaching maximum values of coherence. Moreover, it can be alternatively built up by using weaker but collective interaction with several two-level systems. This approach surpasses the coherence generated by the engineered system-bath coupling for comparable interaction strengths and directly reduces phase estimation error in quantum sensing. This represents a necessary step towards the autonomous quantum sensing.
Environment-induced steady-state quantum coherence (SSQC) is a captivating phenomenon that challenges conventional understandings of decoherence. In this article, we delve into the foundational aspects of environment-induced SSQC, shedding light on its emergence within the framework of system-bath interactions. Starting from a microscopic system-bath-coupled model, we investigate the dependence of SSQC on environmental memory effects, the bath temperature, the system-bath coupling strength, and squeezing parameters. Our findings reveal that the environment not only acts as a generator but also as a disruptor of SSQC. A peak will exist for a non-Markovian bath, which is a result of competition between these two mechanisms. Interestingly, the peak disappears in the Markovian case. Additionally, we observe that the generated SSQC can be further amplified through environment squeezing.
Based on the quantum coherence theory, we employ the [Formula: see text]-norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit’s tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters.