arXiv subjects

Vladimir Gritsev

Publications and source records attributed to Vladimir Gritsev.

At least 55 records · Page 3Linked to original sources

arXiv2014

Topologically protected strongly-correlated states of photons

Hybrid photonic nanostructures allow the engineering of novel interesting states of light. One recent example is topological photonic crystals where a nontrivial Berry phase of the photonic band structure gives rise to topologically protected unidirectionally-propagating (chiral) edge states of photons. Here we demonstrate that by coupling an array of emitters to the chiral photonic edge state one can create strongly correlated states of photons in a highly controllable way. These are topologically protected and have a number of remarkable universal properties: The outcome of scattering does not depend on the positions of emitters and is given only by universal numbers, the zeroes of Laguerre polynomials; two-photon correlation functions manifest a well-pronounced even-odd effect with respect to the number of emitters, and the result of scattering is robust with respect to fluctuations in the emitters' transition frequencies.

quant-ph↗

arXiv2014

Exceptional and regular spectra of a generalized Rabi model

We study the spectrum of the generalized Rabi model in which co- and counter-rotating terms have different coupling strengths. It is also equivalent to the model of a two-dimensional electron gas in a magnetic field with Rashba and Dresselhaus spin-orbit couplings. Like in case of the Rabi model, the spectrum of the generalized Rabi model consists of the regular and the exceptional parts. The latter is represented by the energy levels which cross at certain parameters' values which we determine explicitly. The wave functions of these exceptional states are given by finite order polynomials in the Bargmann representation. The roots of these polynomials satisfy a Bethe ansatz equation of the Gaudin type. At the exceptional points the model is therefore quasi-exactly solvable. An analytical approximation is derived for the regular part of the spectrum in the weak- and strong-coupling limits. In particular, in the strong-coupling limit the spectrum consists of two quasi-degenerate equidistant ladders.

quant-ph↗

arXiv2014

Competing interactions in semiconductor quantum dots

We introduce an integrability-based method enabling the study of semiconductor quantum dot models incorporating both the full hyperfine interaction as well as a mean-field treatment of dipole-dipole interactions in the nuclear spin bath. By performing free induction decay and spin echo simulations we characterize the combined effect of both types of interactions on the decoherence of the electron spin, for external fields ranging from low to high values. We show that for spin echo simulations the hyperfine interaction is the dominant source of decoherence at short times for low fields, and competes with the dipole-dipole interactions at longer times. On the contrary, at high fields the main source of decay is due to the dipole-dipole interactions. In the latter regime an asymmetry in the echo is observed. Furthermore, the non-decaying fraction previously observed for zero field free induction decay simulations in quantum dots with only hyperfine interactions, is destroyed for longer times by the mean-field treatment of the dipolar interactions.

cond-mat.str-el↗

arXiv2014

Supersymmetry in quantum optics and in spin-orbit coupled systems

Light-matter interaction is naturally described by coupled bosonic and fermionic subsystems. This suggests that a certain Bose-Fermi duality is naturally present in the fundamental quantum mechanical description of photons interacting with atoms. We reveal submanifolds in parameter space of a basic light-matter interacting system where this duality is promoted to a supersymmetry (SUSY) which remains unbroken. We show that SUSY is robust with respect to decoherence and dissipation. In particular, a stationary density matrix at the supersymmetric lines in the parameter space has a degenerate subspace. A dimension of this subspace is given by the Witten index and thus topologically protected. As a consequence of this SUSY, dissipative dynamics at the supersymmetric lines is constrained by an additional conserved quantity which translates some part of information about an initial state into the stationary state subspace. We also demonstrate a robustness of this additional conserved quantity away from the supersymmetric lines. In addition, we demonstrate that the same SUSY structures are present in condensed matter systems with spin-orbit couplings of Rashba and Dresselhaus types, and therefore spin-orbit coupled systems at the SUSY lines should be robust with respect to various types of disorder and decoherences. Our findings suggest that optical and condensed matter systems at the SUSY points can be used for quantum information technology and can open an avenue for quantum simulation of the SUSY field theories.

quant-ph↗

arXiv2014

Exact out-of-equilibrium central spin dynamics from integrability

We consider a Gaudin magnet (central spin model) with a time-dependent exchange couplings. We explicitly show that the Schrödinger equation is analytically solvable in terms of generalized hypergeometric functions for particular choices of the time dependence of the coupling constants. Our method establishes a new link between this system and the SU(2) Wess-Zumino-Witten model, and sheds new light on the implications of integrability in out-of-equilibrium quantum physics. As an application, a driven four-spin system is studied in detail.

cond-mat.str-el↗

arXiv2013

Dynamically generated darkness in the Dicke model

We study the dynamics of a driven Dicke model, where the collective spin is rotated with a constant velocity around a fixed axis. The time evolution of the mean photon number and of the atomic inversion is calculated using, on the one hand, a numerical technique for the quantum dynamics of a small number of two-level atoms, on the other hand, time-dependent mean-field theory for the limit of a large number of atoms. We observe a reduction of the mean photon number as compared to its equilibrium value. This dynamically generated darkness is particularly pronounced slightly above the transition to a superradiant phase. We attribute the effect to a slowing down of the motion in the classical limit of a large ensemble and to an interplay of dynamic and geometric phases in the quantum case.

quant-ph↗

arXiv2013

Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems

We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite number of the usual exponentials. This procedure leads to a set of stochastic differential equations on the group manifold, which can be further formulated in terms of the supersymmetric effective action. This action has the form of the Witten topological field theory in the continuum limit. As a consequence, we show how it can be used to obtain the exact results for a specific quantum many-body system which can be otherwise solved only by the Bethe ansatz. To our knowledge this represents the first example of a many-body system treated exactly using the path integral formulation. Moreover, our method can deal with time-dependent parameters, which we demonstrate explicitly.

cond-mat.str-el↗

arXiv2013

Non-equilibrium dynamics of the Tavis-Cummings model

In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between near-integrable and chaotic systems. Here we propose to describe the off-equilibrium dynamics of the Tavis-Cummings model by an underlying classical Hamiltonian system, which can be analyzed using the powerful tools of classical theory of motion. We show that scattering in the classical phase space can drive the quantum model close to thermal equilibrium. Interestingly, this happens in the fully quantum regime, where physical observables do not show any dynamic chaotic behavior.

math-ph↗

arXiv2013

Classifying and measuring the geometry of the quantum ground state manifold

From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have highlighted the role of its symmetric counterpart, the quantum metric tensor. In this paper, we perform a detailed analysis of the ground state Riemannian geometry induced by the metric tensor, using the quantum XY chain in a transverse field as our primary example. We focus on a particular geometric invariant -- the Gaussian curvature -- and show how both integrals of the curvature within a given phase and singularities of the curvature near phase transitions are protected by critical scaling theory. For cases where the curvature is integrable, we show that the integrated curvature provides a new geometric invariant, which like the Chern number characterizes individual phases of matter. For cases where the curvature is singular, we classify three types -- integrable, conical, and curvature singularities -- and detail situations where each type of singularity should arise. Finally, to connect this abstract geometry to experiment, we discuss three different methods for measuring the metric tensor, namely via integrating a properly weighted noise spectral function and by using leading order responses of the work distribution to ramps and quenches in quantum many-body systems.

cond-mat.stat-mech↗

arXiv2013

Full counting statistics of photons interacting with emitter

A complete characterization of quantum fluctuations in many-body systems is accessible through the full counting statistics. We present an exact computation of statistical properties of light in a basic model of light-matter interaction: a multimode photonic field coupled to a single two-level emitter. We mostly consider an initial coherent state in a given mode and demonstrate how the original Poissonian statistics gets modified because of quantum many-body scattering effects leading to non-Poissonian distributions. We argue that measuring this statistics in a simple quantum optical setup provides an insight into many-body correlation effects with photons.

quant-ph↗

arXiv2012

Dynamics of the rotated Dicke model

We study quantum dynamics of the rotationally driven Dicke model where the collective spin is rotated around the z axis with a finite velocity. In the absence of the rotating wave approximation we observe that for several physically relevant initial states the position of the quantum critical point is shifted by the amount given by the applied rotation velocity. This allows us to probe the quantum criticality "from a distance" in parameter space without actual crossing of the quantum critical surface but instead by encircling it in the parameter space. This may provide a useful experimental hint since the quantum state is not destroyed by this protocol. Moreover, for the coherent initial state we observe an interesting non-equilibrium reentrant phenomenon of quantum critical behavior as a function of the driving velocity and construct a non-equilibrium phase diagram of the driven model.

quant-ph↗

arXiv2012

Liouville coherent states

For a certain class of open quantum systems there exists a dynamical symmetry which connects different time-evolved density matrices. We show how to use this symmetry for dynamics in the Liouville space with time-dependent parameters. This allows us to introduce a concept of generalized coherent states (e.g. density matrices) in the Liouville space. Dynamics of this class of density matrices is characterized by robustness with respect to any time-dependent perturbations of the couplings. We study their dynamical context while focusing on common physical situations corresponding to compact and non-compact symmetries.

quant-ph↗

arXiv2012

Scattering of massless particles in one-dimensional chiral channel

We present a general formalism describing a propagation of an arbitrary multiparticle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism is based on a direct and exact resummation of diagrammatic series for the multiparticle scattering matrix. It is complimentary to the Bethe Ansatz and to approaches based on equations of motion, and it reveals a simple and transparent structure of scattering states. In particular, we demonstrate how this formalism works on various examples, including scattering of one- and two-photon states off two- and three-level emitters, off an array of emitters as well as scattering of coherent light. We argue that this formalism can be constructively used for study of scattering of an arbitrary initial photonic state off emitters with arbitrary degree of complexity.

quant-ph↗

arXiv2012

Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models

In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only reduce the number of relevant states in the Hilbert space by a non negligible fraction, they also allow to write the relevant equations in the form of sparse matrix equations. Moreover, we introduce a new inversion method based on a basis of barycentric polynomials which leads to a more stable and efficient root extraction which most importantly avoids the necessity of working with arbitrary precision. As an example we show the results of our procedure applied to the Richardson model on a square lattice.

cond-mat.mes-hall↗

arXiv2012

Geometric phase contribution to quantum non-equilibrium many-body dynamics

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, non-adiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. We show that this interplay can lead to a non-equilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum critical point.

cond-mat.other↗

arXiv2011

Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the coupling strength no longer appear explicitly. The problem is thus reduced to a set of quadratic algebraic equations. The required inverse transformation can then be realized using only linear operations and a standard polynomial root finding algorithm. The method is applied to Richardson's fermionic pairing model, the central spin model and generalized Dicke model.

cond-mat.mes-hall↗

arXiv2010

Scaling approach to quantum non-equilibrium dynamics of many-body systems

Understanding non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of non-equilibrium dynamics of many-body systems, which allow reliable theoretical analysis, are few and far between. In this paper we discuss a broad class of time-dependent interacting systems subject to external linear and parabolic potentials, for which the many-body Schrödinger equation can be solved using a scaling transformation. We demonstrate that scaling solutions exist for both local and nonlocal interactions and derive appropriate self-consistency equations. We apply this approach to several specific experimentally relevant examples of interacting bosons in one and two dimensions. As an intriguing result we find that weakly and strongly interacting Bose-gases expanding from a parabolic trap can exhibit very similar dynamics.

cond-mat.quant-gas↗

arXiv2010

Exact methods in analysis of nonequilibrium dynamics of integrable models: application to the study of correlation functions in nonequilibrium 1D Bose gas

In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operator we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions. In both cases we observe a tendency toward formation of crystal-like correlations at intermediate time scales.

cond-mat.quant-gas↗