Fermionic Bath Research Articles

Keldysh approach to periodically driven systems with a fermionic bath: Nonequilibrium steady state, proximity effect, and dissipation

We study properties of a periodically driven system coupled to a thermal bath. As a nontrivial example, we consider periodically driven metallic system coupled to a superconducting bath. The effect of the superconductor on the driven system is two-fold: it (a) modifies density of states in the metal via the proximity effect and (b) acts as a thermal bath for light-excited quasi-particles. Using Keldysh formalism, we calculate, nonpertubatively in the system-bath coupling, the steady-state properties of the system and obtain non-equilibrium distribution function. The latter allows one to calculate observable quantities which can be spectroscopically measured in tunneling experiments.

Convergence of high order perturbative expansions in open system quantum dynamics.

We propose a new method to directly calculate high order perturbative expansion terms in open system quantum dynamics. They are first written explicitly in path integral expressions. A set of differential equations are then derived by extending the hierarchical equation of motion (HEOM) approach. As two typical examples for the bosonic and fermionic baths, specific forms of the extended HEOM are obtained for the spin-boson model and the Anderson impurity model. Numerical results are then presented for these two models. General trends of the high order perturbation terms as well as the necessary orders for the perturbative expansions to converge are analyzed.

Decoherence of an impurity in a one-dimensional fermionic bath with mass imbalance

We study the transport, decoherence and dissipation of an impurity interacting with a bath of free fermions in a one-dimensional lattice. Numerical simulations are made with the time-evolving block decimation method. We introduce a mass imbalance between the impurity and bath particles and find that the fastest decoherence occurs for a light impurity in a bath of heavy particles. By contrast, the fastest dissipation of energy occurs when the masses are equal. We present a simple model for decoherence in the heavy bath limit, and a linear density response description of the interaction which predicts maximum dissipation for equal masses.

Thermal bath of Dirac field in non-inertial frames

The properties of inertial Dirac thermal bath viewed from the perspective of a uniformly accelerated observer is investigated. Using the single-mode approximation, we obtain the expression of the thermal reduced density matrix, which is constructed by the effective partition function in another way compared with the case of scalar field. We deduce the spectrum of particles and antiparticles seen by Rob and antiRob, respectively. It is found that the fermionic thermal bath will suppress the appearance of Unruh particles.

Anderson-Holstein model in two flavors of the noncrossing approximation

The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on spectral and transport properties is explored in equilibrium, for nonequilibrium steady state and for transient dynamics after a quench. Both the particle-hole symmetric and the more generic particle-hole asymmetric cases are studied. The treatment is based on two complementary noncrossing approximations, the first of which is constructed around the weak-coupling limit and the second around the polaron limit. In general, the two methods disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The frameworks used here can form the starting point for numerically exact methods based on bold-line continuous-time quantum Monte Carlo algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

Photoelectric converters with quantum coherence.

Photon impingement is capable of liberating electrons in electronic devices and driving the electron flux from the lower chemical potential to higher chemical potential. Previous studies hinted that the thermodynamic efficiency of a nanosized photoelectric converter at maximum power is bounded by the Curzon-Ahlborn efficiency η_{CA}. In this study, we apply quantum effects to design a photoelectric converter based on a three-level quantum dot (QD) interacting with fermionic baths and photons. We show that, by adopting a pair of suitable degenerate states, quantum coherences induced by the couplings of QDs to sunlight and fermion baths can coexist steadily in nanoelectronic systems. Our analysis indicates that the efficiency at maximum power is no longer limited to η_{CA} through manipulation of carefully controlled quantum coherences.

Excitations and impurity dynamics in a fermionic Mott insulator with nearest-neighbor interactions

We study analytically and with the numerical time-evolving block decimation method the dynamics of an impurity in a bath of spinless fermions with nearest-neighbor interactions in a one-dimensional lattice. The bath is in a Mott insulator state with alternating sites occupied and the impurity interacts with the bath by repulsive on-site interactions. We find that when the magnitudes of the on-site and nearest-neighbor interactions are close to each other, the system shows excitations of two qualitatively distinct types. For the first type, a domain wall and an antidomain wall of density propagate into opposite directions, while the impurity stays at the initial position. For the second one, the impurity is bound to the antidomain wall while the domain wall propagates, an excitation where the impurity and bath are closely coupled.

Microscopic theory of heat transfer between two fermionic thermal baths mediated by a spin system.

In this paper we have presented the heat exchange between the two fermionic thermal reservoirs which are connected by a fermionic system. We have calculated the heat flux using solution of the c-number Langevin equation for the system. Assuming small temperature difference between the baths we have defined the thermal conductivity for the process. It first increases as a nonlinear function of average temperature of the baths to a critical value then decreases to a very low value such that the heat flux almost becomes zero. There is a critical temperature for the fermionic case at which the thermal conductivity is maximum for the given coupling strength and the width of the frequency distribution of bath modes. The critical temperature grows if these quantities become larger. It is a sharp contrast to the Bosonic case where the thermal conductivity monotonically increases to the limiting value. The change of the conductivity with increase in width of the frequency distribution of the bath modes is significant at the low temperature regime for the fermionic case. It is highly contrasting to the Bosonic case where the signature of the enhancement is very prominent at high temperature limit. We have also observed that thermal conductivity monotonically increases as a function of damping strength to the limiting value at the asymptotic limit. There is a crossover between the high and the low temperature results in the variation of the thermal conductivity as a function of the damping strength for the fermionic case. Thus it is apparent here that even at relatively high temperature, the fermionic bath may be an effective one for the strong coupling between system and reservoir. Another interesting observation is that at the low temperature limit, the temperature dependence of the heat flux is the same as the Stefan-Boltzmann law. This is similar to the bosonic case.

Description of non-Markovian effect in open quantum system with the discretized environment method

An approach, called discretized environment method, is introduced to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of discretized states with an appropriate coupling to the system of interest. The finite set of system plus environment degrees of freedom are then explicitly followed in time leading to a quasi-exact description. The present approach is anticipated to be particularly accurate in the low temperature and strongly non-Markovian regime. The discretized environment method is validated on a two-level system (qubit) coupled to a bosonic or fermionic heat bath. A perfect agreement with the quantum Langevin approach is found. Further illustrations are made on a three-level system (qutrit) coupled to a bosonic heat-bath. Emerging processes due to strong memory effects are discussed.

Fermionic-mode entanglement in non-Markovian environment

We evaluate the non-Markovian effects on the entanglement dynamics of a fermionic system interacting with two dissipative vacuum reservoirs. The exact solution of density matrix is derived by utilizing the Feynman–Vernon influence functional theory in the fermionic coherent state representation and the Grassmann calculus, which are valid for both the fermionic and bosonic baths, and their difference lies in the dependence of the parity of the initial states. The fermionic entanglement dynamics is presented by adding an additional restriction to the density matrix known as the superselection rules. Our analysis shows that the usual decoherence suppression schemes implemented in qubits systems can also be achieved for systems of identical fermions, and the initial state proves its importance in the evolution of fermionic entanglement. Our results provide a potential way to decoherence controlling of identical fermions.

Nonequilibrium Dynamics of a Periodically-driven Impurity Spin Coupled to the Bath of Ultracold Fermions by Kondo Coupling

The dynamics of the anisotropic Kondo model under the periodic driving is studied. The periodic driving we consider is the local magnetic field which couples with the impurity spin and the in-plane exchange interaction. At the special point in the parameter space (Toulouse limit), the anisotropic Kondo model can be transformed to the non-interacting resonant level model and thereby the exact results for arbitrary external fields can be obtained. It is shown that characteristic behavior of the dynamics changes with the field intensity, the field frequency, and the Kondo temperature. When the local magnetic field intensity is very large compared with the field frequency and the Kondo temperature, the time dependence of the impurity spin and the spin density of the fermionic bath shows an oscillation whose period is inversely proportional to the field intensity. We also find that another time scale, which is given by the inverse of the Kondo temperature, governs the response of the system to the external field.

Transport signatures of Majorana quantum criticality realized by dissipative resonant tunneling

We consider theoretically the transport properties of a spinless resonant electronic level coupled to strongly dissipative leads, in the regime of circuit impedance near the resistance quantum. Using the Luttinger liquid analogy, one obtains an effective Hamiltonian expressed in terms of interacting Majorana fermions, in which all environmental degrees of freedom (leads and electromagnetic modes) are encapsulated in a single fermionic bath. General transport equations for this system are then derived in terms of the Majorana $T\text{-matrix}$. A perturbative treatment of the Majorana interaction term yields the appearance of a marginal, linear dependence of the conductance on temperature when the system is tuned to its quantum critical point, in agreement with recent experimental observations. We investigate in detail the different crossovers involved in the problem, and analyze the role of the interaction terms in the transport scaling functions. In particular, we show that single barrier scaling applies when the system is slightly tuned away from its Majorana critical point, strengthening the general picture of dynamical Coulomb blockade.

Correlated parity measurements as a probe of non-Abelian statistics in one-dimensional superconducting wires

We propose a method to detect a signature of non-abelian statistics in a 1D superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase, and a total of 4 Majorana particles. We show that an appropriately timed "pulse" in the coupling between the two middle Majoranas leads to a coherent rotation of the two q-bits associated with the pairs of Majoranas in the two TSC segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be used to rotate spins in NMR. This can be exploited both to probe the correlations of the Majoranas, and to manipulate the Majorana q-bits, in these 1D wires. We discuss the experimental requirements for such a coherent rotation to be observable when the wire system is coupled to a fermionic bath.

Optimized dynamical control of state transfer through noisy spin chains

We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.

Nonequilibrium entropic temperature and its lower bound for quantum stochastic processes.

In this paper, we have studied the Shannon "entropic" nonequilibrium temperature (NET) of quantum Brownian systems. The Brownian particle is attached to either a bosonic or fermionic bath. Based on the Fokker-Planck description of the c-number quantum Langevin equation, we have calculated entropy production, NET, and their bounds. Entropy production (EP), the upper bound of entropy production (UBEP), and the deviation of the UBEP from EP monotonically decrease as functions of time to equilibrium value for both of the thermal baths. The deviation decreases with increase of temperature of the bosonic thermal bath, but it becomes larger as the temperature of the fermionic bath grows. We also observe that nonequilibrium temperature and its lower bound monotonically increase to equilibrium value with the progression of time. But their difference as a function of time shows an optimum behavior in most cases. Finally, we have observed that at long time, the entropic temperature (for a bosonic thermal bath) first increases nonlinearly as a function of thermodynamic temperature (TT) and, if the TT is appreciably large, then it grows linearly. But for the fermionic thermal bath, the entropic temperature decreases monotonically as a nonlinear function of thermodynamic temperature to zero value.

A fermionic bath induced antibunching and coherence in Mollow spectra

In this work, we have derived the modified Bloch equation from the generalized master equation due to the fermionic bath where one needs to consider Grassmann algebra to obtain the similar mathematical structure of the reduced system dynamics, as in the case of a bosonic bath. There is an enhancement of antibunching in the photon emission with an increase in effective temperature. This is in principle a manifestation of the antisymmetric two-particle dynamic anticorrelation in the fermionic bath with a defined chemical potential characterized by the forbidden overlapping. This is evident from the modified fluctuation–dissipation relation. We have compared it thoroughly with an experimental result in the temperature dependent emission characteristics within an environment of quantum dots in a Hanburry-Brown–Twiss set-up. For the fermionic bath, an effective temperature assisted coherence phenomenon is induced in the system dynamics, which is reflected in the resonance fluorescence spectrum with the variation of chemical potential. In the Mollow's absorption spectra, when the Rabi frequency is sufficiently low, the side peaks appear as chemical potential induced coherence phenomenon rather than the traditional field induced one. The subsequent gain in the probe wave is evidently of thermal origin, where the energy is fully supplied by the fermionic bath at non-zero temperatures. This is not possible for a bosonic bath—an example of the extraction of coherence from the fermionic bath.

Dissipative Dynamics of a Driven Quantum Spin Coupled to a Bath of Ultracold Fermions

We explore the dynamics and the steady state of a driven quantum spin coupled to a bath of fermions, which can be realized with a strongly imbalanced mixture of ultracold atoms using currently available experimental tools. Radio-frequency driving can be used to induce tunneling between the spin states. The Rabi oscillations are modified due to the coupling of the quantum spin to the environment, which causes frequency renormalization and damping. The spin-bath coupling can be widely tuned by adjusting the scattering length through a Feshbach resonance. When the scattering potential creates a bound state, by tuning the driving frequency it is possible to populate either the ground state, in which the bound state is filled, or a metastable state in which the bound state is empty. In the latter case, we predict an emergent inversion of the steady-state magnetization. Our work shows that different regimes of dissipative dynamics can be explored with a quantum spin coupled to a bath of ultracold fermions.

Quantum criticality in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction

We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like |\epsilon|^r at the Fermi energy (\epsilon=0) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to |\omega|^s. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<1/2 and 1/2<s<1, and applying the numerical renormalization-group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and \omega/T scaling in the dynamics that characterize an interacting critical point. The (r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum critical point.

Entanglement of nanoelectromechanical oscillators by Cooper-pair tunneling

We demonstrate that entanglement of two macroscopic nanoelectromechanical resonators---coupled to each other via a common detector, a tunnel junction---can be generated by running a current through the device. We introduce a setup that overcomes generic limitations of proposals suggesting to entangle systems via a shared bath. At the heart of the proposal is an Andreev entangler setup, representing an experimentally feasible way of entangling two nanomechanical oscillators. Instead of relying on the coherence of a (fermionic) bath, in the Andreev entangler setup, a split Cooper pair that coherently tunnels to each oscillator mediates their coupling and thereby induces entanglement between them. Since entanglement is in each instance generated by Markovian and non-Markovian noisy open system dynamics in an out-of-equilibrium situation, we argue that the present scheme also opens up perspectives to observe dissipation-driven entanglement in a condensed-matter system.

Dynamics of an impurity in a one-dimensional lattice

We study the non-equilibrium dynamics of an impurity in a harmonic trap that is kicked with a well-defined quasi-momentum, and interacts with a bath of free fermions or interacting bosons in a one-dimensional lattice configuration. Using numerical and analytical techniques we investigate the full dynamics beyond linear response, which allows us to quantitatively characterize states of the impurity in the bath for different parameter regimes. These vary from a tightly bound molecular state in a strongly interacting limit to a polaron (dressed impurity) and a free particle for weak interactions, with composite behaviour in the intermediate regime. These dynamics and different parameter regimes should be readily realizable in systems of cold atoms in optical lattices.