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Interaction with environment as a source of ultra-strong coupling

Timofey T. Sergeev, I. V. Vovchenko, A. A. Zyablovsky, Evgenii S. Andrianov

Published Aug 16, 2021• 0 citations
OpenAlex

Abstract

In this letter, we demonstrate that in both classical and quantum open systems, the Hamiltonian interaction between subsystems, along with relaxations caused by the interaction with reservoirs, results in the appearance of effective non-Hermitian coupling. It is determined by a gradient of density of states of reservoirs. We show that for a power-law frequency dependence of the density of states, the non-Hermitian coupling is proportional to a product of the Hermitian coupling strength and the relaxation rates. As a result, this non-Hermitian coupling begins to play a crucial role with increasing Hermitian coupling strength between the subsystems and leads to a qualitative change in the behavior of non-Hermitian systems. Namely, when the Hermitian coupling strength exceeds a critical value, the non-Hermitian coupling becomes so large that it guarantees that the system is in the strong coupling regime at any relaxation rate. This critical coupling can be associated with the transition point to the ultra-strong coupling regime, which, until now, has not been defined exactly.

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In this letter, we demonstrate that in both classical and quantum open systems, the Hamiltonian interaction between subsystems, along with relaxations caused by the interaction with reservoirs, results in the appearance of effective non-Hermitian coupling. It is determined by a gradient of density of states of reservoirs. We show that for a power-law frequency dependence of the density of states, the non-Hermitian coupling is proportional to a product of the Hermitian coupling strength and the relaxation rates. As a result, this non-Hermitian coupling begins to play a crucial role with increasing Hermitian coupling strength between the subsystems and leads to a qualitative change in the behavior of non-Hermitian systems. Namely, when the Hermitian coupling strength exceeds a critical value, the non-Hermitian coupling becomes so large that it guarantees that the system is in the strong coupling regime at any relaxation rate. This critical coupling can be associated with the transition point to the ultra-strong coupling regime, which, until now, has not been defined exactly.
Recently, strong coupling between non-Hermitian physical systems of different nature is widely investigated due to it endows them with new properties. In this work, we investigate the energy transport between strongly coupled systems. We use a partial-secular approach for the description of an open quantum system to investigate the system dynamics during the transition from a weak to a strong coupling regime with an increase of coupling between subsystems. On the example of strongly coupled two-level atoms, we show that near the transition point enhancement of energy transport between the system and reservoirs takes place. This manifests in the fact that energy flow normalized to the coupling constant reaches the maximum both in the cases of zero and non-zero frequency detuning. We show that maximization of normalized energy flow can be used for the determination of the transition to the strong coupling regime in the case of non-zero detuning when there is no clear transition point from the weak to strong coupling regime. The suppression of the energy flow at high relaxation is demonstrated.
In this paper we review an approach to the dynamics of open quantum systems based of non-Hermitian Hamiltonians. Non-Hermitian Hamiltonians arise naturally when one wish to study a subsystem interacting with a continuum of states. Moreover, quantum subsystems with probability sinks or sources are naturally described by non-Hermitian Hamiltonians. Herein, we discuss a non-Hermitian formalism based on the density matrix. We show both how to derive the equations of motion of the density matrix and how to define statistical averages properly. It turns out that the laws of evolution of the normalized density matrix are intrinsically non-linear. We also show how to define correlation functions and a non-Hermitian entropy with a non zero production rate. The formalism has been generalized to the case of hybrid quantum-classical systems using a partial Wigner representation. The equations of motion and the statistical averages are defined analogously to the pure quantum case. However, the definition of the entropy requires to introduce a non-Hermitian linear entropy functional.
In this work we investigate the late-time steady states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is nonvanishing or equivalently if the relaxation time scales are finite. Using a variety of nonequilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system+environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multitime correlations of the open system evolve towards those of the closed system thermal state. Multitime correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.
Decoherence is strongly influenced by environmental criticality, with conventional Hermitian critical points typically enhancing the loss of quantum coherence. Here, we show that this paradigm is fundamentally altered in non-Hermitian environments. Focusing on qubits coupled to non-Hermitian spin chains and interacting ultracold Fermi gases, we find that approaching exceptional points can either enhance or strongly suppress decoherence, depending on the balance between Hermitian and non-Hermitian system-environment couplings. In particular, when these couplings are comparable, decoherence is dramatically suppressed at exceptional transitions. We trace this behavior to the distinct response of the environmental ground state near non-Hermitian degeneracies and demonstrate the robustness of this effect across multiple models. Finally, we show that the predicted suppression of decoherence is directly observable on current digital quantum simulation platforms. Our results establish exceptional points as a concrete mechanism for suppressing decoherence and identify non-Hermitian criticality as a new avenue for coherence control in open quantum systems and quantum technologies.
In this paper, we investigate the open tight-binding model with NNN sites coupled to two reservoirs on its edges with the nonequilibrium Green function method to understand effects of open boundaries. As a result, we obtain an analytical expression of the electron density in the steady state and in the transient regime for N→∞N \rightarrow \inftyN→∞ and at absolute zero temperature. From the expression of the electron density in the steady state, we show that the open boundaries do not affect the qualitative behavior of the electron density and the phase transition which has been observed for the isolated tight-binding model also exists in our open case. Using the expression of the time-dependent electron density, we show that a two-step decay appears in the relaxation process purely caused by open boundaries. In addition, we show that the dependence of speed of convergence on boundary coupling strength qualitatively changes at a certain value of the boundary parameters. This is a result of special eigenvalues of a non-hermitian matrix whose imaginary parts do not vanish even in the limit N→∞N \rightarrow \inftyN→∞.
A general thermodynamic framework is presented for open quantum systems in fixed contact with a thermal reservoir. The first and second law are obtained for arbitrary system-reservoir coupling strengths, and including both factorized and correlated initial conditions. The thermodynamic properties are adapted to the generally strong coupling regime, approaching the ones defined for equilibrium, and their standard weak-coupling counterparts as appropriate limits. Moreover, they can be inferred from measurements involving only system observables. Finally, a thermodynamic signature of non-Markovianity is formulated in the form of a negative entropy production rate.