arXiv subjects

Nikolai A. Sinitsyn

Publications and source records attributed to Nikolai A. Sinitsyn.

At least 37 records · Page 2Linked to original sources

arXiv2021

Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory

We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. The results predict a dynamic phase transition, and show that similarly-looking models belong to different topological classes.

cond-mat.mes-hall↗

arXiv2020

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

A time-reversed dynamics unwinds information scrambling, which is induced during the time-forward evolution with a complex Hamiltonian. We show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

quant-ph↗

arXiv2020

Integrable multistate Landau-Zener models with parallel energy levels

We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/τ$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discussed completely solvable MLZ Hamiltonians.

math-ph↗

arXiv2020

Multitime Landau-Zener model: classification of solvable Hamiltonians

We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number $N$ of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system's dynamics. Due to the possibility of such a detailed classification, the multitime Landau-Zener (MTLZ) model defines a useful special function of theoretical physics.

math-ph↗

arXiv2018

A large class of solvable multistate Landau-Zener models and quantum integrability

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians. Within the multistate Landau-Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models. Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number $N\ge 4$ of interacting states and shows a quickly growing with $N$ number of exact adiabatic energy crossing points, which appear at different moments of time. At each $N$, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with $N$ quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.

quant-ph↗

arXiv2017

Integrable time-dependent quantum Hamiltonians

We formulate a set of conditions under which dynamics of a time-dependent quantum Hamiltonian are integrable. The main requirement is the existence of a nonabelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time-dependence into various quantum integrable models, so that the resulting non-stationary Schrodinger equation is exactly solvable. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

quant-ph↗

arXiv2017

Multistate Landau-Zener models with all levels crossing at one point

We discuss common properties and reasons for integrability in the class of multistate Landau-Zener (MLZ) models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a dual one, whose scattering matrix can be also obtained analytically. For applications, we demonstrate how our results can be used to study conversion of molecular into atomic Bose condensates during passage through the Feshbach resonance, and provide purely algebraic solutions of the bowtie and special cases of the driven Tavis-Cummings model (DTCM).

quant-ph↗

arXiv2017

Landau-Zener extension of the Tavis-Cummings model: structure of the solution

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and $q$-deformed binomial statistics.

quant-ph↗

arXiv2017

Nearly-optimal quantum control: analytical approach

We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for optimization. This optimization strategy can be preferred in practice because it is physically transparent and does not lead to combinatorial complexity in multistate problems. For demonstration, we design optimized control protocols that achieve switching between orthogonal states of a naturally biased quantum two-level system.

quant-ph↗

arXiv2017

The Quest for Solvable Multistate Landau-Zener Models

Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.

quant-ph↗

arXiv2016

Solvable multistate model of Landau-Zener transitions in cavity QED

We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

cond-mat.mes-hall↗

arXiv2016

Dynamic Symmetries and Quantum Nonadiabatic Transitions

Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. We generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. We also discuss applications of this result to the multistate Landau-Zener (LZ) theory.

quant-ph↗

arXiv2015

Quantum Fingerprints in Higher Order Correlators of a Spin Qubit

The spin of an electron in a semiconductor quantum dot represents a natural nanoscale solid state qubit. Coupling to nuclear spins leads to decoherence that limits the number of allowed quantum logic operations for this qubit. Traditional approach to characterize decoherence is to explore spin Relaxation and the spin echo, which are equivalent to the studies of the spins 2nd order time-correlator at various external conditions. Here we develop an alternative technique by showing that considerable information about dynamics can be obtained from direct measurements of higher than the 2nd order correlators, which to date have been hindered in semiconductor quantum dots. We show that such correlators are sensitive to pure quantum effects that cannot be explained within the classical framework, and which allow direct determination of ensemble and quantum dephasing times with only repeated projective measurements without the need for coherent spin control. Our method enables studies of pure quantum effects, including tests of the Leggett-Garg type inequalities that rule out local hidden variable interpretation of the spin qubit dynamics.

cond-mat.mes-hall↗

arXiv2015

Long-lived nanosecond spin relaxation and spin coherence of electrons in monolayer MoS_2 and WS_2

The recently-discovered monolayer transition metal dichalcogenides (TMDCs) provide a fertile playground to explore new coupled spin-valley physics. Although robust spin and valley degrees of freedom are inferred from polarized photoluminescence (PL) experiments, PL timescales are necessarily constrained by short-lived (3-100ps) electron-hole recombination. Direct probes of spin/valley polarization dynamics of resident carriers in electron (or hole) doped TMDCs, which may persist long after recombination ceases, are at an early stage. Here we directly measure the coupled spin-valley dynamics in electron-doped MoS_2 and WS_2 monolayers using optical Kerr spectroscopy, and unambiguously reveal very long electron spin lifetimes exceeding 3ns at 5K (2-3 orders of magnitude longer than typical exciton recombination times). In contrast with conventional III-V or II-VI semiconductors, spin relaxation accelerates rapidly in small transverse magnetic fields. Supported by a model of coupled spin-valley dynamics, these results indicate a novel mechanism of itinerant electron spin dephasing in the rapidly-fluctuating internal spin-orbit field in TMDCs, driven by fast intervalley scattering. Additionally, a long-lived spin coherence is observed at lower energies, commensurate with localized states. These studies provide crucial insight into the physics underpinning spin and valley dynamics of resident electrons in atomically-thin TMDCs.

cond-mat.mtrl-sci↗

arXiv2014

Cross-correlation spin noise spectroscopy of heterogeneous interacting spin systems

We develop and apply a minimally invasive approach for characterization of inter-species spin interactions by detecting spin fluctuations alone. We consider a heterogeneous two-component spin ensemble in thermal equilibrium that interacts via binary exchange coupling, and we determine cross-correlations between the intrinsic spin fluctuations exhibited by the two species. Our theoretical predictions are experimentally confirmed using `two-color' optical spin noise spectroscopy on a mixture of interacting Rb and Cs alkali vapors. The results allow us to explore the rates of spin exchange and total spin relaxation under conditions of strict thermodynamic equilibrium.

cond-mat.mes-hall↗

arXiv2014

Quantum Zeno effect as a topological phase transition in full counting statistics and spin noise spectroscopy

When the interaction of a quantum system with a detector is changing from weak to strong coupling limits, the system experiences a transition from the regime with quantum mechanical coherent oscillations to the regime with a frozen dynamics. In addition to this quantum Zeno transition, we show that the full counting statistics of detector signal events experiences a topological phase transition at the boundary between two phases at intermediate coupling of a quantum system to the detector. We demonstrate that this transition belongs to the class of topological phase transitions that can be classified by elements of the braid group. We predict that this transition can be explored experimentally by means of the optical spin noise spectroscopy.

cond-mat.mes-hall↗

arXiv2013

Higher Order Spin Noise Statistics

The optical spin noise spectroscopy (SNS) is a minimally invasive route towards obtaining dynamical information about electrons and atomic gases by measuring mesoscopic time-dependent spin fluctuations. Recent improvements of the sensitivity of SNS should make it possible to observe higher order spin correlators at thermodynamic equilibrium. We develop theoretical methods to explore higher order (3rd and 4th) cumulants of the spin noise in the frequency domain. We make predictions for the possible functional form of these correlators in single quantum dot experiments and then apply the method of the stochastic path integral to estimate effects of many-body interactions.

cond-mat.mes-hall↗

arXiv2013

Spin noise spectroscopy of quantum dot molecules

We discuss advantages and limitations of the spin noise spectroscopy for characterization of interacting quantum dot systems on specific examples of individual singly and doubly charged quantum dot molecules (QDMs). It is shown that all the relevant parameters of the QDMs including tunneling amplitudes with spin-conserving and spin-non-conserving interactions, decoherence rates, Coulomb repulsions, anisotropic g-factors and the distance between the dots can be determined by measuring properties of the spin noise power spectrum.

cond-mat.mes-hall↗