arXiv subjects

N. A. Sinitsyn

Publications and source records attributed to N. A. Sinitsyn.

At least 19 recordsLinked to original sources

arXiv2026

Multivariable Painleve'-II equation: connection formulas for asymptotic solutions

For an integrable generalization of the Painleve'-II equation (P-II) to a system of coupled equations with symmetry breaking terms, an asymptotically exact WKB analysis is applied to obtain connection formulas for solutions at different infinities. The analysis relies on an exact solution of the quantum mechanical Demkov--Osherov model (DOM), revealing a possible deeper relation between classical integrable systems and solvable multistate Landau--Zener models. An application of the connection formulas to the problem of unstable vacuum decay during a second-order phase transition provides precise scaling of the number of excitations, including subdominant contributions.

math-ph↗

arXiv2023

Phase transition in fluctuations of interacting spins at infinite temperature

The high temperature limit of interacting spins is usually not associated with ordering or critical phenomena. Nevertheless, spontaneous fluctuations of a local spin polarization at equilibrium have nontrivial dynamics even in this limit. Here, we demonstrate that the spin noise power spectrum of these fluctuations can undergo discontinuous changes as a function of an external magnetic field. As a simple illustration, we consider a model of Ising-like long range spin-spin interactions with a transverse magnetic field as a control parameter. This system undergoes a phase transition associated with disappearance of the noise power peak responsible for the most detrimental decoherence effect of the interactions. \end{abstract}

cond-mat.stat-mech↗

arXiv2021

Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. We show how such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New fully solvable MLZ systems are also found.

quant-ph↗

arXiv2020

Dynamic spin localization and gamma-magnets

We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the simplest such models, which can be realized with localized states in Dirac materials, satisfy integrability conditions that we use to describe pseudospin dynamics in a linearly time-dependent magnetic field. Generalizing to an arbitrary number of qubits, we construct a spin Hamiltonian, which we call the gamma-magnet. This system does not conserve polarization of any spin and the net spin polarization. Nevertheless, for arbitrarily strong interactions, nonadiabatic dynamics, and any initial eigenstate, we find that quantum interference suppresses spin-flips. This behavior resembles many-body localization but occurs in phase space of many spins rather than real space. This effect may not have a counterpart in classical physics and can be a signature of a new type of spin ordering, which is different from both disordered spin glasses and ordered phases of spin lattices.

cond-mat.mes-hall↗

arXiv2019

Cooperative Light Emission in the Presence of Strong Inhomogeneous Broadening

We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time-dependence. The analysis shows that, regardless the distribution of energy level splittings, a sharp phase transition occurs between the weak and strong cooperative emission phases near a critical photonic frequency sweeping rate. The associated scaling exponent is determined. We suggest that this phase transition can be observed in an ensemble of negatively charged NV centers in diamond interacting with a microwave half-wavelength cavity mode even in the regime of weak coupling and at strong disorder of two-level splittings.

cond-mat.mes-hall↗

arXiv2018

Quantum annealing and thermalization: insights from integrability

We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including a scaling of their number with the annealing rate and the system size. We prove that quantum correlations can accelerate computations and, at the end of the annealing protocol, lead to the perfect Gibbs distribution of all microstates.

quant-ph↗

arXiv2018

Broadband spectroscopy of thermodynamic magnetization fluctuations through a ferromagnetic spin-reorientation transition

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar$^+$ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, $S(ν)$, exhibits a remarkably robust $ν^{-3/2}$ power law over frequencies $ν$ from 1~kHz to 1~MHz. As the SRT region is traversed, however, $S(ν)$ spectra develop a steadily-increasing critical frequency, $ν_0$, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

cond-mat.mtrl-sci↗

arXiv2017

Computing with a single qubit faster than the computation quantum speed limit

The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error correction strategies that protect such computations.

quant-ph↗

arXiv2017

Exact transition probabilities in a six-state Landau-Zener system with path interference

We identify a nontrivial multistate Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the Landau-Zener formula. We discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.

quant-ph↗

arXiv2017

Constraints on scattering amplitudes in multistate Landau-Zener theory

We derive a set of constraints, which we will call hierarchy constraints (HCs), on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix.

quant-ph↗

arXiv2016

The Theory of Spin Noise Spectroscopy: A Review

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical Spin Noise Spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside with examples of their applications.

cond-mat.mes-hall↗

arXiv2016

Quantized beam shifts in graphene

We predict quantized Imbert-Fedorov, Goos-Hänchen, and photonic spin Hall shifts for light beams impinging on a graphene-on-substrate system in an external magnetic field. In the quantum Hall regime the Imbert-Fedorov and photonic spin Hall shifts are quantized in integer multiples of the fine structure constant $α$, while the Goos- Hänchen ones in multiples of $α^2$. We investigate the influence on these shifts of magnetic field, temperature, and material dispersion and dissipation. An experimental demonstration of quantized beam shifts could be achieved at terahertz frequencies for moderate values of the magnetic field.

physics.optics↗

arXiv2016

Solvable 4-state Landau-Zener model of two interacting qubits with path interference

We identify a nontrivial 4-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. We argue that this system satisfies the criteria of integrability in the multistate Landau-Zener theory, which allows us to derive explicit exact analytical expressions for the transition probability matrix. We also argue that this model is likely a special case of a larger class of solvable systems, and present a 6-state generalization as an example.

cond-mat.mes-hall↗

arXiv2016

Universality in higher order spin noise spectroscopy

Higher order time-correlators of spontaneous spin fluctuations reveal the information about spin interactions. We argue that in a broad class of spin systems one can justify a phenomenological approach to explore such correlators. Thus, we predict that the 3rd and 4th order spin cumulants are described by a universal function that can be parametrized by a small set of parameters. We show that the fluctuation theorem constrains this function so that such correlators are fully determined by lowest nonlinear corrections to the free energy and the mean and variance of microscopic spin currents. We also provide an example of microscopic calculations for conduction electrons.

cond-mat.stat-mech↗

arXiv2015

Higher order spin noise spectroscopy of atomic spins in fluctuating external fields

We discuss the effect of external noisy magnetic fields on mesoscopic spin fluctuations that can be probed in semiconductors and atomic vapors by means of optical spin noise spectroscopy (SNS). We show that conventional arguments of the law of large numbers do not apply to spin correlations induced by external fields, namely, the magnitude of the 4th order spin cumulant grows as $\sim N^2$ with the number $N$ of observed spins, i.e. it is not suppressed in comparison to the 2nd order cumulant. This allows us to design a simple experiment to measure the 4th order cumulant of spin fluctuations in an atomic system near thermodynamic equilibrium and develop quantitative theory that explains all observations.

cond-mat.mes-hall↗

arXiv2015

Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance

We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the Inverse Faraday Effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can also escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly regardless the shape of the resonance. We also discuss extension of our results to multistate systems.

cond-mat.mes-hall↗

arXiv2015

Three stage decoherence dynamics of electron spin qubits in an optically active quantum dot

The control of discrete quantum states in solids and their use for quantum information processing is complicated by the lack of a detailed understanding of the mechanisms responsible for qubit decoherences. For spin qubits in semiconductor quantum dots, phenomenological models of decoherence currently recognize two Basic stages; fast ensemble dephasing due to the coherent precession of spin qubits around nearly static but randomly distributed hyperfine fields and a much slower process of irreversible relaxation of spin qubit polarization due to dynamics of the nuclear spin bath induced by complex many-body interaction effects. We unambiguosly demonstrate that such a view on decoherence is greatly oversimplified; the relaxation of a spin qubit state is determined by three rather than two basic stages. The additional stage corresponds to the effect of coherent dephasing processes that occur in the nuclear spin bath that manifests itself by a relatively fast but incomplete non-monotonous relaxation of the central spin polarization at intermediate timescales. This observation changes our understanding of the electron spin qubit decoherence mechanisms in solid state systems.

cond-mat.mes-hall↗

arXiv2014

Exact results for models of multichannel quantum nonadiabatic transitions

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\hat{H}(t) = \hat{A} +\hat{B} t + \hat{C}/t$, where $t$ is time and $\hat{A}$, $\hat{B}$, $\hat{C}$ are Hermitian $N\times N$ matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at $t \rightarrow -\infty$. This allows one to continue such solutions analytically to $t \rightarrow +\infty$, and connect their asymptotic behavior at $t \rightarrow -\infty$ and $t \rightarrow +\infty$. This property becomes particularly useful when a model shows additional discrete symmetries. In particular, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.

cond-mat.mes-hall↗