We investigate the dynamics of entanglement between the system and the environment during thermalization of a noninteracting fermionic impurity coupled to a fermionic thermal bath. We show that transient entanglement can be observed even in the weak coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. This entanglement vanishes for long times, but is preserved over timescales comparable to the relaxation time. Its magnitude depends only weakly on the system-environment coupling but instead strongly on the purity of the initial state of the system. We relate the presence of such transient entanglement to the unitary character of the system-bath dynamics underlying the reduced Markovian description.
We investigate the dynamics of entanglement between the system and the environment during thermalization of a noninteracting fermionic impurity coupled to a fermionic thermal bath. We show that transient entanglement can be observed even in the weak coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. This entanglement vanishes for long times, but is preserved over timescales comparable to the relaxation time. Its magnitude depends only weakly on the system-environment coupling but instead strongly on the purity of the initial state of the system. We relate the presence of such transient entanglement to the unitary character of the system-bath dynamics underlying the reduced Markovian description.
We investigate the behavior of entanglement between a single fermionic level and a fermionic bath in three distinct thermodynamic regimes. First, in thermal equilibrium, we analyze the dependence of entanglement on the considered statistical ensemble: for the grand canonical state, it is generated only for a sufficiently strong system-bath coupling, whereas it is present for arbitrarily weak couplings for the canonical state with a fixed particle number. The threshold coupling strength at which entanglement appears is shown to strongly depend on the bath bandwidth. Second, we consider the relaxation to equilibrium. In this case a transient entanglement in a certain time interval can be observed even in the weak-coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. At strong-coupling strengths, entanglement is preserved for long times and converges to its equilibrium value. Finally, in voltage-driven junctions, a steady-state entanglement is generated for arbitrarily weak system-bath couplings at a certain threshold voltage. It is enhanced in the strong-coupling regime, and it is reduced by either the particle-hole or the tunnel coupling asymmetry.
We consider a central fermion strongly interacting with a surrounding mesoscopic bath of fermions which is weakly coupled to a Markovian bath of fermions. The master equation of the system consisting of the central fermion and the mesoscopic bath is derived, and based on this master equation, the reduced dynamics and thermalization of the central fermion are investigated. As probes for studying the dynamics and thermalization, the mean number of the central fermion and the current density are calculated. The observed dynamics reveal that strong coupling strength induces non-Markovian behavior and that in the long time limit thermalization is attained leaving the central fermion in a thermal state that is described by the corresponding Gibbs distribution. Upon attaining the thermal state, the central fermion is found to be entangled with the collective mode of the surrounding mesoscopic bath in the high-temperature regime, whereas in the low-temperature regime, it is found to undergo sudden death of entanglement.
Coupling to a thermal bath leads to thermalisation and decoherence of stored quantum information. For a system of Gaussian fermions, the fermionic analog of linear or Gaussian optics, these dynamics can be elegantly and efficiently described by evolution of the system's covariance matrix. Taking both system and bath to be Gaussian fermionic, we observe that thermalization and decoherence occurs at a rate that is independent of the bath temperature. Furthermore, we also consider a weak coupling regime where the dynamics are Markovian. We present a microscopic derivation of Markovian master equations entirely in the language of covariance matrices, where temperature independence remains manifest. This is radically different from behaviour seen in other scenarios, such as when fermions interact with a bosonic bath. Our analysis applies to many Majorana fermion systems that have been heralded as very robust, topologically protected, qubits. In these systems, it has been claimed that thermal decoherence can be exponentially suppressed by reducing temperature, but we find Gaussian decoherence cannot be cooled away.
Coupling to a thermal bath leads to decoherence of stored quantum information. For a system of Gaussian fermions, the fermionic analog of linear or Gaussian optics, these dynamics can be elegantly and efficiently described by evolution of the system's covariance matrix. Taking both system and bath to be Gaussian fermionic, we observe that decoherence occurs at a rate that is independent of the bath temperature. Furthermore, we also consider a weak coupling regime where the dynamics are Markovian. We present a microscopic derivation of Markovian master equations entirely in the language of covariance matrices, where temperature independence remains manifest. This is radically different from behaviour seen in other scenarios, such as when fermions interact with a bosonic bath. Our analysis applies to many Majorana fermion systems that have been heralded as very robust, topologically protected, qubits. In these systems, it has been claimed that thermal decoherence can be exponentially suppressed by reducing temperature, but we find Gaussian decoherence cannot be cooled away.
Coupling to a thermal bath leads to decoherence of stored quantum information. For a system of Gaussian fermions, the fermionic analog of linear or Gaussian optics, these dynamics can be elegantly and efficiently described by evolution of the system's covariance matrix. Taking both system and bath to be Gaussian fermionic, we observe that decoherence occurs at a rate that is independent of the bath temperature. Furthermore, we also consider a weak coupling regime where the dynamics are Markovian. We present a microscopic derivation of Markovian master equations entirely in the language of covariance matrices, where temperature independence remains manifest. This is radically different from behaviour seen in other scenarios, such as when fermions interact with a bosonic bath. Our analysis applies to many Majorana fermion systems that have been heralded as very robust, topologically protected, qubits. In these systems, it has been claimed that thermal decoherence can be exponentially suppressed by reducing temperature, but we find Gaussian decoherence cannot be cooled away.
An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as coherence and entanglement in the low-temperature regime. However, for sufficiently high temperature and when the number of bath particles approaches the thermodynamic limit, this feature vanishes and the dynamics closely mimics Markovian evolution. The properties of the long-time-averaged state and the trapped information of the initial state for the central qubit are also investigated in detail, confirming that the nonergodicity of the dynamics can be attributed to the finite temperature and finite size of the bath. It is shown that if a certain stringent resonance condition is satisfied, the long-time-averaged state retains quantum coherence, which can have far reaching technological implications in engineering quantum devices. An exact time-local master equation of the canonical form is derived. With the help of this master equation, the nonequilibrium properties of the central spin system are studied by investigating the detailed balance condition and irreversible entropy production rate. The result reveals that the central qubit thermalizes only in the limit of very high temperature and large number of bath spins.