Keldysh Approach Research Articles

Nonlinear effects in a Floquet-driven optomechanical system

We investigate theoretically the nonlinear effects in a Floquet-driven optomechanical system with quadratic coupling. When the periodically modulated driving field is strong, we establish an effective time-dependent model to describe this system. Using the Keldysh approach, we calculate the retarded Green's function to study the response behavior of the system to external probing. We find that when the $n\mathrm{th}$ sideband of a probe field satisfies the condition of two-phonon resonance, the transparency window occurs. In addition, we find some abnormal behaviors of the output field, which have no counterpart in the standard optomechanical models. These results provide a promising platform for controlling light propagation and light manipulation operations which have potential applications in quantum precision measurement techniques.

First-principles scattering with Büttiker probes: The role of self-energies

Understanding electronic transport properties is important for designing devices for applications. Many studies rely on the semiclassical Boltzmann approach within the relaxation time approximation. This method delivers a graphic physical picture of the scattering process, but in some cases it lacks full quantum-mechanical effects. Here, we use a non-equilibrium Green's function Korringa-Kohn-Rostoker (KKR) method with phase-breaking scattering via virtual B\"uttiker terminals as a fully quantum mechanical approach to transport phenomena. With this, we assess the validity of the relation of the self-energy $\mathrm{\ensuremath{\Sigma}}$ to the scattering time $\ensuremath{\tau}$, often used in literature in the case of constant relaxation time approximation. We argue that the scattering time does not affect the thermopower in the Boltzmann approach and thus should take no effect either on the thermopower calculated via the Keldysh approach. We find a nearly linear relation for the transmission function ${T}_{S}({E}_{F},\mathrm{\ensuremath{\Sigma}})$ of free electrons and Cu with respect to $\frac{1}{\mathrm{\ensuremath{\Sigma}}}$. However, we find that this is not the case for Pd. We attribute this to neighboring states contributing due to the additional broadening via the self-energy $\mathrm{\ensuremath{\Sigma}}$. These findings suggest that a simple identification of scattering time and self-energy is not sufficient. Finally, we discuss the benefits and limits of the application of the virtual terminal approach.

Signature of universal fast scrambling in the transient response of a driven mott insulator system

The scrambling rate λ s, a measure of the early growth of decoherence in an interacting quantum system, has been conjectured to have a universal saturation bound, λ s ⩽ 2πk B T/ℏ, where T is the temperature. This decoherence arises from the spread of quantum information over a large number of untracked degrees of freedom. The commonly studied indicator of scrambling is the out of time-ordered correlator (OTOC) of noncommuting quantum operators, in-turn related to generalized uncertainty relations, and reminiscent of the Lyapunov exponent of classically chaotic systems. From a practical measurement point of view, other quantities besides OTOCs, that are also sensitive to these generalized uncertainty relations, may capture the scrambling behavior. Here, using a large- Keldysh field theory approach, we show that the nonequilibrium current response of a Mott insulator system consisting of a mesoscopic quantum dot array, when subjected to an electric field quench, reveals this phenomenon on account of number-phase uncertainty. Both ac and dc field quenches are considered. The passage from the initial Mott insulator phase with well-defined charge excitations, to the final nonequilibrium steady current state, is revealed in the transient current response that has Bloch-like oscillations. We find that the amplitude of these oscillations decreases at the universal rate, 2πk B T/ℏ, associated with fast scramblers. Our Mott insulator model provides a new example of a fast scrambler in addition to the known ones such as extremal black holes and the Sachdev–Ye–Kitaev (SYK) model.

Spectral characterization of non-Gaussian quantum noise: Keldysh approach and application to photon shot noise

Having accurate tools to describe non-classical, non-Gaussian environmental fluctuations is crucial for designing effective quantum control protocols and understanding the physics of underlying quantum dissipative environments. We show how the Keldysh approach to quantum noise characterization can be usefully employed to characterize frequency-dependent noise, focusing on the quantum bispectrum (i.e., frequency-resolved third cumulant). Using the paradigmatic example of photon shot noise fluctuations in a driven bosonic mode, we show that the quantum bispectrum can be a powerful tool for revealing distinctive non-classical noise properties, including an effective breaking of detailed balance by quantum fluctuations. The Keldysh-ordered quantum bispectrum can be directly accessed using existing noise spectroscopy protocols.

Topological Field Theory Far from Equilibrium.

The observable properties of topological quantum matter are often described by topological field theories. Here, we demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional driven open dynamics with a Chern insulator steady state. Within a Keldysh field theory approach, we show that under mild assumptions-particle number conservation and purity of the stationary state-an abelian Chern-Simons theory describes its response to external perturbations. As a corollary, we predict chiral edge modes stabilized by a dissipative bulk.

Evaporation dynamics of the Sachdev-Ye-Kitaev model

In this paper, we study the evaporation dynamics of the Sachdev-Ye-Kitaev (SYK) model, with an initial temperature $T_\chi$, by coupling it to a thermal bath with lower temperature $T_\psi<T_\chi$ modeled by a larger SYK model. The coupling between the small system and the bath is turned on at time $t=0$. Then the system begins to envolve and finally becomes thermalized. Using the Keldysh approach, we analyze the relaxation process of the system for different temperatures and couplings. For marginal or irrelevant coupling, after a short-time energy absorption, we find a smooth thermalization of the small system where the energy relaxes before the system become thermalized. The relaxation rate of effective temperature is found to be bounded by $T$, while the energy thermalization rate increases without saturation when increasing the coupling strength. On the contrary, for the relevant coupling case, both energy and effective temperature show oscillations. We find this oscillations frequency to be coincident with the excitation energy of a Majorana operator.

Higgs oscillations in time-resolved optical conductivity

Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Non-equilibrium superconductors are often studied using time resolved optical conductivity measurements. Thus, the characterization of a superconducting state in a pump driven non-equilibrium state requires careful attention in the time domain. We calculate time-resolved optical conductivity of a pumped superconducting state using a non-equilibrium Keldysh approach. Through functional derivation, the optical conductivity is obtained with full vertex corrections and used to characterize the transient superconducting state. The transient optical conductivity shows the suppression of the superconducting order parameter in the time domain. The subsequent recovery of the order parameter exhibits oscillatory behavior that corresponds to the Higgs amplitude mode, and may be seen in several parts of the spectrum.

Quantum chaos for the unitary Fermi gas from the generalized Boltzmann equations

In this paper, we study the chaotic behavior of the unitary Fermi gas in both high- and low-temperature limits by calculating the quantum Lyapunov exponent defined in terms of the out-of-time-order correlator. We take the method of generalized Boltzmann equations, derived from the augmented Keldysh approach (Aleiner et al 2016 Ann. Phys. 375, 378). At high temperatures, the system is described by weakly interacting fermions with two spin components and the Lyapunov exponent is found to be . Here n is the density of fermions for a single-spin component. In the low-temperature limit, the system is a superfluid and can be described by phonon modes. Using the effective action derived in (Son and Wingate 2006 Ann. Phys. 321, 197), we find where TF is the Fermi energy. By comparing these to existing results of heat conductivity, we find that where DE is the energy diffusion constant and v is some typical velocity. We argue that this is related to the conservation law for such systems with quasi-particles.

Analyzing the spectral density of a perturbed analog quantum simulator using the Keldysh formalism

Simulation of interacting electron systems is one of the great challenges of modern quantum chemistry and solid state physics. Controllable quantum systems offer the opportunity to create artificial structures which mimic the system of interest. An interesting quantity to extract from these quantum simulations is the spectral function. We map a noisy quantum simulator onto a fermionic system and investigate the influence of decoherence on the simulation of the spectral density using a diagrammatic approach on Keldysh contour. We show that features stronger than the single-qubit decoherence rate can be resolved, while weaker features wash out. For small systems, we compare our Keldysh approach to master-equation calculations.

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.

Self-consistent Keldysh approach to quenches in the weakly interacting Bose-Hubbard model

We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemented numerically by a parallelized code. We exploit this approach to study the correlation propagation after a quench in the interaction parameter, for one (1D) and two (2D) dimensions. In particular, we show how our approach is able to recover the crossover from ballistic to diffusive regime by increasing the boson-boson interaction. Finally we also discuss the role of a thermal initial state on the dynamics both for 1D and 2D Bose Hubbard models, finding that surprisingly at high temperature a ballistic evolution is restored.

Heat transport in nonuniform superconductors

We calculate electronic energy transport in inhomogeneous superconductors using a fully self-consistent nonequilibrium quasiclassical Keldysh approach. We develop a general theory and apply it to a superconductor with an order parameter that forms domain walls of the type encountered in the Fulde-Ferrell-Larkin-Ovchinnikov state. The heat transport in the presence of a domain wall is inherently anisotropic and nonlocal. The bound states in the nonuniform region play a crucial role and control heat transport in several ways: (i) they modify the spectrum of quasiparticle states and result in Andreev reflection processes and (ii) they hybridize with the impurity band and produce a local transport environment with properties very different from those in a uniform superconductor. As a result of this interplay, heat transport becomes highly sensitive to temperature, magnetic field, and disorder. For strongly scattering impurities, we find that the transport across domain walls at low temperatures is considerably more efficient than in the uniform superconducting state.

Tunable photonic cavity coupled to a voltage-biased double quantum dot system: Diagrammatic nonequilibrium Green's function approach

We investigate gain in microwave photonic cavities coupled to voltage-biased double quantum dot systems with an arbitrary strong dot-lead coupling and with a Holstein-like light-matter interaction, by adapting the diagrammatic Keldysh nonequilibrium Green's function approach. We compute out-of-equilibrium properties of the cavity : its transmission, phase response, mean photon number, power spectrum, and spectral function. We show that by the careful engineering of these hybrid light-matter systems, one can achieve a significant amplification of the optical signal with the voltage-biased electronic system serving as a gain medium. We also study the steady state current across the device, identifying elastic and inelastic tunnelling processes which involve the cavity mode. Our results show how recent advances in quantum electronics can be exploited to build hybrid light-matter systems that behave as single-atom amplifiers and photon source devices. The diagrammatic Keldysh approach is primarily discussed for a cavity-coupled double quantum dot architecture, but it is generalizable to other hybrid light-matter systems.

Korshunov instantons out of equilibrium

Zero-dimensional dissipative action possesses non-trivial minima known as Korshunov instantons. They have been known so far only for imaginary time representation that is limited to equilibrium systems. In this work we reconstruct and generalise Korshunov instantons using real-time Keldysh approach. This allows us to formulate the dissipative action theory for generic non-equilibrium conditions. Possible applications of the theory to transport in strongly biased quantum dots are discussed..

NUMERICAL SIMULATION OF ELECTRIC CHARACTERISTICS OF DEEP SUBMICRON SILICON-ON-INSULATOR MOS TRANSISTOR

Today submicron silicon-on-insulator (SOI) MOSFET structures are widely used in different electronic components and also can be used as sensing elements in some applications. The development of devices based on the structures with specified characteristics is impossible without computer simulation of their electric properties. The latter is not a trivial task since many complicated physical processes and effects must be taken into account. In current study ensemble Monte Carlo simulation of electron and hole transport in deep submicron n-channel SOI MOSFET with 100 nm channel length is performed. The aim of the study is investigation of the influence of interband impact ionization process on the device characteristics and determination of the transistor operation modes when impact ionization process starts to make an appreciable influence on the device functioning. Determination of the modes is very important for adequate and accurate modeling of different devices on the basis of SOI MOSFET structures. Main focus thereby is maid on the comparison of the use of two models of impact ionization process treatment with respect to their influence on the transistor current-voltage characteristics. The first model is based on the frequently used Keldysh approach and the other one utilizes the results obtained via numerical calculations of silicon band structure. It is shown that the use of Keldysh impact ionization model leads to much faster growth of the drain current and provides earlier avalanche breakdown for the SOI MOSFET. It is concluded that the choice between the two considered impact ionization models may be critical for simulation of the device electric characteristics.

Floquet-Boltzmann equation for periodically driven Fermi systems

Periodically driven quantum systems can be used to realize quantum pumps, ratchets, artificial gauge fields and novel topological states of matter. Starting from the Keldysh approach, we develop a formalism, the Floquet-Boltzmann equation, to describe the dynamics and the scattering of quasiparticles in such systems. The theory builds on a separation of time-scales. Rapid, periodic oscillations occurring on a time scale $T_0=2 \pi/\Omega$, are treated using the Floquet formalism and quasiparticles are defined as eigenstates of a non-interacting Floquet Hamiltonian. The dynamics on much longer time scales, however, is modelled by a Boltzmann equation which describes the semiclassical dynamics of the Floquet-quasiparticles and their scattering processes. As the energy is conserved only modulo $\hbar \Omega$, the interacting system heats up in the long-time limit. As a first application of this approach, we compute the heating rate for a cold-atom system, where a periodical shaking of the lattice was used to realize the Haldane model.

Multiple-photon absorption in cooled molecular beams of acenes compounds at 266 and 355 nm laser radiation

SynopsisThe cooled molecular beams of acenes compounds as naphthalene C10H8, anthracene C14H10, and ben- zantracene C18H12, were produced by adiabatic expansion in high vacuum chamber, 10-8 torr. Molecular beams interacted with laser radiation of 266 and 355 nm, from a Ng:YAG laser at intensities up to 1010 W·cm-2 At higher intensities the multiple photon absorption was possible. The number of photons was calculated using Keldysh approach. The dominant photophysics of photon-molecule interactions were photodissociation and photoionization processes depending on the wavelength used during the experiment.

Probing Majorana physics in quantum-dot shot-noise experiments

We consider a quantum dot coupled to a topological superconductor and two normal leads and study transport properties of the system. Using Keldysh path-integral approach, we study current fluctuations (shot noise) within the low-energy effective theory. We argue that the combination of the tunneling conductance and the shot noise through a quantum dot allows one to distinguish between the topological (Majorana) and non-topological (e.g., Kondo) origin of the zero-bias conduction peak. Specifically, we show that, while the tunneling conductance might exhibit zero-bias anomaly due to Majorana or Kondo physics, the shot noise is qualitatively different in the presence of Majorana zero modes.

Quantum kinetics of ultracold fermions coupled to an optical resonator

We study the far-from-equilibrium statistical mechanics of periodically driven fermionic atoms in a lossy optical resonator. We show that the interplay of the Fermi surface with cavity losses leads to sub-natural cavity linewidth narrowing, squeezed light, and out-of-equilibrium quantum statistics of the atoms. Adapting the Keldysh approach, we set-up and solve a quantum kinetic Boltzmann equation in a systematic $1/N$ expansion with $N$ the number of atoms. In the strict thermodynamic limit $N,V\rightarrow \infty$, $N/V=\text{const.}$ we find the atoms (fermions or bosons) remain immune against cavity-induced heating or cooling. At next-to-leading order in $1/N$, we find a "one-way thermalization" of the atoms determined by cavity decay. We argue that, in absence of an equilibrium fluctuation-dissipation relation, the long-time limit $\Delta t \rightarrow \infty$ does not commute with the thermodynamic limit $N\rightarrow \infty$, such that for the physically relevant case of large but finite $N$, the dynamics ultimately becomes strongly coupled, especially close to the superradiance phase transition.

Dynamic chaos in the tunnelling ionization produced by a strong low-frequency electromagnetic field

Ionization of atoms by a strong low-frequency linearly polarized electromagnetic field (the photon energy is small compared to the atomic ionization potential) is considered under new conditions compared to the well known Keldysh approach. The field strength is supposed to be small in comparison to the atomic field strength. But the Coulomb interaction of an electron with atomic core is assumed to be of the same order of magnitude as the interaction between an electron and the external electromagnetic field. It was shown that then classical electron motion in the continuum becomes chaotic (this is so-called dynamic chaos). Using the averaging procedure of Chirikov about the chaotic variation of the phase of motion, the considered Newton problem is transformed into the problem of nonlinear electron diffusion over energy scale. In this work we derive the classical electron energy averaged over fast chaotic oscillations of an electron in the final continuum state which takes into account both the Coulomb field and electromagnetic field. This energy is used for analytic calculation of the ionization rate of the ground atomic state into the low lying continuum state based on the Landau–Dykhne approximation (with exponential accuracy). We found that the ionization rate depends significantly on the field frequency. When field frequency decreases, the well known tunnelling limit has been obtained, and then the ionization rate does not depend on the field frequency.