arXiv subjects

Denys I. Bondar

Publications and source records attributed to Denys I. Bondar.

At least 73 records · Page 4Linked to original sources

arXiv2021

Non-Uniqueness of Non-Linear Optical Response

In recent years, non-linear optical phenomena have attracted much attention, with a particular focus on the engineering and exploitation of non-linear responses. Comparatively little study has however been devoted to the driving fields that generate these responses. In this work, we demonstrate that the relationship between a driving field and the optical response it induces is non-unique. Using a generic model for a strongly interacting system, we show that multiple candidate driving field exists, which will all generate the same response. Consequently, it is possible show that the optical response is not sufficient to determine the internal dynamics of the system, and that different solutions for the driving field will do different amounts of work on a system. This non-uniqueness phenomenon may in future be utilised to engineer internal system states without modifying its optical response.

physics.optics↗

arXiv2021

Optical Indistinguishability via Twinning Fields

Here we introduce the concept of the twinning field -- a driving electromagnetic pulse that induces an identical optical response from two distinct materials. We show that for pairs of generic many-body systems, a twinning field which renders the systems \emph{optically indistinguishable} always exists. The conditions under which this field is unique are derived, and this analysis is supplemented by numerical calculations of twinning fields for the Fermi-Hubbard model. The universal existence of twinning fields may lead to new research directions in non-linear optics, materials science, and quantum technologies.

cond-mat.str-el↗

arXiv2021

Decoherence-Free Entropic Gravity: Model and Experimental Tests

Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless free parameter $σ$ goes to infinity, the entropic master equation recovers conservative gravity. We show that the proposed master equation is fully compatible with the \textit{q}\textsc{Bounce} experiment for ultra-cold neutrons as long as $σ\gtrsim 250$ at $90\%$ confidence. Furthermore, the entropic master equation predicts energy increase and decoherence on long time scales and for large masses, phenomena which tabletop experiments could test. In addition, comparing entropic gravity's energy increase to that of the Diósi-Penrose model for gravity induced decoherence indicates that the two theories are incompatible. These findings support the theory of entropic gravity, motivating future experimental and theoretical research.

quant-ph↗

arXiv2021

Diffusion Fails to Make a Stink

In this work we consider the question of whether a simple diffusive model can explain the scent tracking behaviours found in nature. For this behaviour to occur, both the concentration of a scent and its gradient must be above some threshold. Applying these conditions to the solutions of various diffusion equations, we find that a purely diffusive model cannot simultaneously satisfy the tracking conditions when parameters are in the experimentally observed range. This demonstrates the necessity of modelling odor dispersal with full fluid dynamics, where non-linear phenomena such as turbulence play a critical role.

cond-mat.soft↗

arXiv2020

Robust polarimetry via convex optimization

We present mathematical methods, based on convex optimization, for correcting non-physical coherency matrices measured in polarimetry. We also develop the method for recovering the coherency matrices corresponding to the smallest and largest values of the degree of polarization given the experimental data and a specified tolerance. We use experimental non-physical results obtained with the standard polarimetry scheme and a commercial polarimeter to illustrate these methods. Our techniques are applied in post-processing, which complements other experimental methods for robust polarimetry.

physics.optics↗

arXiv2020

How to Win Friends and Influence Functionals: Deducing Stochasticity From Deterministic Dynamics

The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. In this review, we introduce the influence functional formalism in both the quantum and classical regimes. Using this technique, we demonstrate how irreversible behaviour arises generically from the reduced microscopic dynamics of a system-environment amalgam. The influence functional is then used to rigorously derive stochastic equations of motion from a microscopic Hamiltonian. In this method stochastic terms are not identified heuristically, but instead arise from an exact mapping only available in the path-integral formalism. The interpretability of the individual stochastic trajectories arising from the mapping is also discussed. As a consequence of these results, we are also able to show that the proper classical limit of stochastic quantum dynamics corresponds non-trivially to a generalised Langevin equation derived with the classical influence functional. This provides a further unifying link between open quantum systems and their classical equivalent, highlighting the utility of influence functionals and their potential as a tool in both fundamental and applied research.

cond-mat.stat-mech↗

arXiv2020

Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation

We introduce a new technique for the simulation of dissipative quantum systems. This method is composed of an approximate decomposition of the Lindblad equation into a Kraus map, from which one can define an ensemble of wavefunctions. Using principal component analysis, this ensemble can be truncated to a manageable size without sacrificing numerical accuracy. We term this method \emph{Ensemble Rank Truncation} (ERT), and find that in the regime of weak coupling, this method is able to outperform existing wavefunction Monte-Carlo methods by an order of magnitude in both accuracy and speed. We also explore the possibility of combining ERT with approximate techniques for simulating large systems (such as Matrix Product States (MPS)), and show that in many cases this approach will be more efficient than directly expressing the density matrix in its MPS form. We expect the ERT technique to be of practical interest when simulating dissipative systems for quantum information, metrology and thermodynamics.

quant-ph↗

arXiv2020

Quantum and semiclassical dynamics as fluid theories where gauge matters

The family of trajectories-based approximations employed in computational quantum physics and chemistry is very diverse. For instance, Bohmian and Heller's frozen Gaussian semiclassical trajectories seem to have nothing in common. Based on a hydrodynamic analogy to quantum mechanics, we furnish the unified gauge theory of all such models. In the light of this theory, currently known methods are just a tip of the iceberg, and there exists an infinite family of yet unexplored trajectory-based approaches. Specifically, we show that each definition for a semiclassical trajectory corresponds to a specific hydrodynamic analogy, where a quantum system is mapped to an effective probability fluid in the phase space. We derive the continuity equation for the effective fluid representing dynamics of an arbitrary open bosonic many-body system. We show that unlike in conventional fluid, the flux of the effective fluid is defined up to Skodje's gauge [R. T. Skodje et. al. Phys. Rev. A 40, 2894 (1989)]. We prove that the Wigner, Husimi and Bohmian representations of quantum mechanics are particular cases of our generic hydrodynamic analogy, and all the differences among them reduce to the gauge choice. Infinitely many gauges are possible, each leading to a distinct quantum hydrodynamic analogy and a definition for semiclassical trajectories. We propose a scheme for identifying practically useful gauges and apply it to improve a semiclassical initial value representation employed in quantum many-body simulations.

quant-ph↗

arXiv2020

Amplification of quadratic Hamiltonians

Speeding up the dynamics of a quantum system is of paramount importance for quantum technologies. However, in finite dimensions and without full knowledge of the details of the system, it is easily shown to be impossible. In contrast we show that continuous variable systems described by a certain class of quadratic Hamiltonians can be sped up without such detailed knowledge. We call the resultant procedure Hamiltonian amplification (HA). The HA method relies on the application of local squeezing operations allowing for amplifying even unknown or noisy couplings and frequencies by acting on individual modes. Furthermore, we show how to combine HA with dynamical decoupling to achieve amplified Hamiltonians that are free from environmental noise. Finally, we illustrate a significant reduction in gate times of cavity resonator qubits as one potential use of HA.

quant-ph↗

arXiv2020

Driven Imposters: Controlling Expectations in Many-Body Systems

We present a framework to control and track the observables of a general solid state system driven by an incident laser field. The main result is a non-linear equation of motion for tracking an observable, together with a constraint on the size of expectations which may be reproduced via tracking. Among other applications, this model provides a potential route to the design of laser fields which cause photo-induced superconductivity in materials above their critical temperature. As a first test, the strategy is used to make the expectation value of the current conform to an arbitrary function under a range of model parameters. Additionally, using two reference spectra for materials in the conducting and insulating regimes respectively, the tracking algorithm is used to make each material mimic the optical spectrum of the other.

quant-ph↗

arXiv2020

Accurate Lindblad-Form Master Equation for Weakly Damped Quantum Systems Across All Regimes

Realistic models of quantum systems must include dissipative interactions with an environment. For weakly-damped systems the Lindblad-form Markovian master equation is invaluable for this task due to its tractability and efficiency. This equation only applies, however, when the frequencies of any subset of the system's transitions are either equal (degenerate), or their differences are much greater than the transitions' linewidths (far-detuned). Outside of these two regimes the only available efficient description has been the Bloch-Redfield (B-R) master equation, the efficacy of which has long been controversial due to its failure to guarantee the positivity of the density matrix. The ability to efficiently simulate weakly-damped systems across all regimes is becoming increasingly important, especially in the area of quantum technologies. Here we solve this long-standing problem. We discover that a condition on the slope of the spectral density is sufficient to derive a Lindblad form master equation that is accurate for all regimes. We further show that this condition is necessary for weakly-damped systems to be described by the B-R equation or indeed any Markovian master equation. We thus obtain a replacement for the B-R equation over its entire domain of applicability that is no less accurate, simpler in structure, completely positive, allows simulation by efficient quantum trajectory methods, and unifies the previous Lindblad master equations. We also show via exact simulations that the new master equation can describe systems in which slowly-varying transition frequencies cross each other during the evolution. System identification tools, developed in systems engineering, play an important role in our analysis. We expect these tools to prove useful in other areas of physics involving complex systems.

quant-ph↗

arXiv2020

Uncomputability and complexity of quantum control

In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e., there is no algorithm that can decide whether dynamics of an arbitrary quantum system can be manipulated by accessible external interactions (coherent or dissipative) such that a chosen target reaches a desired value. This conclusion holds even for the relaxed requirement of the target only approximately attaining the desired value. These findings do not preclude an algorithmic solvability for a particular class of quantum control problems. Moreover, any quantum control problem can be made algorithmically solvable if the set of accessible interactions (i.e., controls) is rich enough. To arrive at these results, we develop a technique based on establishing the equivalence between quantum control problems and Diophantine equations, which are polynomial equations with integer coefficients and integer unknowns. In addition to proving uncomputability, this technique allows to construct quantum control problems belonging to different complexity classes. In particular, an example of the control problem involving a two-mode coherent field is shown to be NP-hard, contradicting a widely held believe that two-body problems are easy.

quant-ph↗

arXiv2019

Controlling Arbitrary Observables in Correlated Many-body Systems

Here we present an expanded analysis of a model for the manipulation and control of observables in a strongly correlated, many-body system, which was first presented in [McCaul et al., eprint: arXiv:1911.05006]. A field-free, non-linear equation of motion for controlling the expectation value of an essentially arbitrary observable is derived, together with rigorous constraints that determine the limits of controllability. We show that these constraints arise from the physically reasonable assumptions that the system will undergo unitary time evolution, and has enough degrees of freedom for the electrons to be mobile. Furthermore, we give examples of multiple solutions to generating target observable trajectories when the constraints are violated. Ehrenfest theorems are used to further refine the model, and provide a check on the validity of numerical simulations. Finally, the experimental feasibility of implementing the control fields generated by this model is discussed.

quant-ph↗

arXiv2019

Koopman wavefunctions and classical-quantum correlation dynamics

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect -- the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive-definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical-quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

math-ph↗

arXiv2019

Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems

Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particles and harmonic systems evolving in a bounded phase-space in such a way that entropy is nonconserved. While these nonconserving states are classically forbidden, they may be interpreted as states of a quantum system tunneling through a potential barrier boundary. In this case, the allowed boundary conditions are the only distinction between classical and quantum systems. We show that the boundary conditions for a tunneling quantum system become the criteria for entropy preservation in the classical limit. These findings highlight how boundary effects drastically change the nature of a system.

cond-mat.stat-mech↗

arXiv2018

Friction as a consistent quantum-mechanical concept

A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant and phenomenological model of dissipation) is known to be in odds with the detailed balance in the thermodynamic limit. We show that this is not the case for quantum systems with internal (e.g. spin) states non-adiabatically coupled to translational dynamics. For such systems, a quantum master equation is derived which phenomenologically accounts for the frictional effect of a uniform zero temperature environment. A simple analytical example is provided. Conjectures regarding the finite temperature case are also formulated. The results are important for efficient simulations of complex molecular dynamics and quantum reservoir engineering applications.

quant-ph↗

arXiv2018

Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit

The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic Ehrenfest theorems by assuming that the coordinates and momenta do not commute. Forbidding creation of antiparticles and requiring the commutativity of the coordinates and momenta lead to classical Spohn's equation [Ann. Phys. {\bf 282}, 420 (2000)]. Moreover, Spohn's equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.

quant-ph↗

arXiv2018

Non-conservative Forces via Quantum Reservoir Engineering

A systematic approach is given for engineering dissipative environments that steer quantum wavepackets along desired trajectories. The methodology is demonstrated with several illustrative examples: environment-assisted tunneling, trapping, effective mass assignment, and pseudo-relativistic behavior. Non-conservative stochastic forces do not inevitably lead to decoherence - we show that purity can be well-preserved. These findings highlight the flexibility offered by non-equilibrium open quantum dynamics.

quant-ph↗