arXiv subjects

Vladimir Y. Chernyak

Publications and source records attributed to Vladimir Y. Chernyak.

At least 19 recordsLinked to original sources

arXiv2025

Pump-intensity-scaling of Two-Photon-Absorption and Photon Statistics of Entangled-Photon Fields

We use a non-perturbative theoretical approach to the parametric down-conversion (PDC) process, which generates entangled-photon field for an arbitrarily strong pump-pulse. This approach can be used to evaluate multi-point field correlation functions to compute nonlinear spectroscopic signals induced by a strong pump. The entangled-photon statistics is studied using Glauber's $g^{(2)}$ function, which helps understand the significance of the photon entanglement-time and the pump-pulse intensity on spectroscopic signals. Under the non-perturbative treatment of the entangled field, the two-photon absorption (TPA) signal shows linear to strongly non-linear growth with the pump intensity, rather than linear to quadratic scaling reported previously. An increase in the range of pump intensity for the linear scaling is observed as the pump band-width is increased. We propose an experimental scheme that can select contributions to the TPA signal that arise solely from interactions with the entangled photons, and filter out unentangled photon contributions, which are dominant at higher pump intensities, paving a way to explore the entanglement effects at higher intensities.

physics.chem-ph↗

arXiv2024

On the rational invariants of quantum systems of $n$-qubits

For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such invariant rational functions is purely transcendental over the complex numbers and has transcendence degree $4^n - 2n-1$. An explicit transcendence basis is also exhibited.

math-ph↗

arXiv2024

On the variety of X-states

We introduce the notion of an X-state on $n$-qubits. After taking the Zariski closure of the set of X-states in the space of all mixed states, we obtain a complex algebraic variety $\scr X$ that is equipped with the action of the Lie group of local symmetries $G$. We show that the field of $G$-invariant rational functions on $\scr X$ is purely transcendental over the complex numbers of degree $2^{2n-1}-n-1$.

math-ph↗

arXiv2023

Rational Local Unitary Invariants of Symmetrically Mixed States of Two Qubits

We compute the field of rational local unitary invariants for locally maximally mixed states and symmetrically mixed states of two qubits. In both cases, we prove that the field of rational invariants is purely transcendental. We also construct explicit geometric quotients and prove that they are always rational. All the results are obtained by working over the field of real numbers, employing methods from classical and geometric invariant theory over arbitrary fields of characteristic zero.

math.AG↗

arXiv2023

Qubit entanglement generated by classical light driving an optical cavity

We study the generation of entanglement between two qubits which communicate through a single cavity mode of quantum light but have no direct interaction. We show that such entanglement can be generated simply by exchanging quanta with a third party, which is in our case the cavity mode. Exchanging only a single quantum creates maximal entanglement. A single quantum can be provided by an external quantum light source. However, we use a classical light source to pump quanta which are used for the exchange, and investigate the degree of two-qubit entanglement. We first identify a characteristic timescale of the interaction between the cavity mode and each qubit. We investigate two regimes of the driving pulse length, one is short and the other is long compared to the characteristic timescale of the interaction. In the first regime, it is known that the pulse can pump the system by generating a displacement of the cavity mode. We show that, by using a specific pulse shape, one can make the displacement to essentially vanish after the pulse finishes interaction with the cavity mode. In this case, a rotation of the qubits can be invoked. In addition, higher-order effects of the pulse including a non-local operation on the joint system of the cavity mode and the qubits are found, and we present a formalism to compute each term up to a given order. An explicit condition on the pulse shape for each term to be nonzero or suppressed is derived to enable an experimental design for verifying the entanglement generation using a classical light source. In the opposite regime where the driving is sufficiently long, we utilize a squeezed state which may be obtained adiabatically. We study how the squeezing and the accompanied rotation of qubits affect the generated two-qubit entanglement.

quant-ph↗

arXiv2023

Effective Rationality for Local Unitary Invariants of Mixed States of Two Qubits

We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality statements for the local unitary invariants of symmetric mixed states of two qubits. Our results apply to both complex-valued and real-valued invariants.

quant-ph↗

arXiv2022

Nonlinear quantum interferometric spectroscopy with entangled photon pairs

We develop closed expressions for a time-resolved photon counting signal induced by an entangled photon pair in an interferometric spectroscopy setup. Superoperator expressions in Liouville-space are derived that can account for relaxation and dephasing induced by coupling to a bath. Interferometric setups mix matter and light variables non-trivially, which complicates their interpretation. We provide an intuitive modular framework for this setup that simplifies its description. Based on separation between the detection stage and the light-matter interaction processes. We show that the pair entanglement time and the interferometric time-variables control the observed physics time-scale. Only a few processes contribute in the limiting case of small entanglement time with respect to the sample response, and specific contributions can be singled out.

quant-ph↗

arXiv2022

Coherent reaction between molecular and atomic Bose-Einstein condensates: integrable model

We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a nonexponential dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate. We find that the emerging phase can have a thermalized energy distribution with the temperature defined by the rate of the transition. This phase, however, has strong purely quantum correlations.

quant-ph↗

arXiv2021

Probability measures on graph trajectories

The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which admits a global bound on its degree and rates. Our approach is elementary. Our main intention is to fill a gap in the literature.

math.PR↗

arXiv2021

Heisenberg-Uncertainty of Spatially-Gated Electromagnetic Fields

A Heisenberg uncertainty relation is derived for spatially-gated electric and magnetic field fluctuations. The uncertainty increases for small gating sizes which implies that in confined spaces the quantum nature of the electromagnetic field must be taken into account. Optimizing the state of light to minimize the electric at the expense of the magnetic field, and vice versa should be possible. Spatial confinements and quantum fields may alternatively be realized without gating by interaction of the field with a nanostructure. Possible applications include nonlinear spectroscopy of nanostructures and optical cavities and chiral signals.

quant-ph↗

arXiv2021

Nonadiabatic Phase Transition with Broken Chiral Symmetry

We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sub-lattices are suppressed in the nearly-adiabatic regime exponentially. Thus, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.

cond-mat.stat-mech↗

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

Hypercurrents

We introduce the notion of a protocol, which consists of a space whose points are labeled by real numbers indexed by the set of cells of a fixed CW complex in prescribed degrees, where the labels are required to vary continuously. If the space is a one-dimensional manifold, then a protocol determines a continuous time Markov chain. When a homological gap condition is present, we associate to each protocol a 'characteristic' cohomology class which we call the hypercurrent. The hypercurrent comes in two flavors: one algebraic topological and the other analytical. For generic protocols we show that the analytical hypercurrent tends to the topological hypercurrent in the low temperature limit. We also exhibit examples of protocols having nontrivial hypercurrent.

math.AT↗

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

On fluctuations of cycles in a finite CW complex

We use algebraic topology to study the stochastic mo- tion of cellular cycles in a finite CW complex. Inspired by statis- tical mechanics, we introduce a homological observable called the average current. The latter measures the average flux of the prob- ability in the process. In the low temperature, adiabatic limit, we prove that the average current fractionally quantizes, in which the denominators are combinatorial invariants of the CW complex.

math.AT↗

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↗