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Bogdan Damski

Publications and source records attributed to Bogdan Damski.

At least 37 records · Page 2Linked to original sources
arXiv2015

The quantum Ising model: finite sums and hyperbolic functions

We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.

quant-ph↗
arXiv2015

Fidelity approach to quantum phase transitions in quantum Ising model

Fidelity approach to quantum phase transitions uses the overlap between ground states of the system to gain some information about its quantum phases. Such an overlap is called fidelity. We illustrate how this approach works in the one dimensional quantum Ising model in the transverse field. Several closed-form analytical expressions for fidelity are discussed. An example of what insights fidelity provides into the dynamics of quantum phase transitions is carefully described. The role of fidelity in central spin systems is pointed out.

quant-ph↗
arXiv2014

Counterdiabatic driving of the quantum Ising model

The system undergoes adiabatic evolution when its population in the instantaneous eigenbasis of its time-dependent Hamiltonian changes only negligibly. Realization of such dynamics requires slow-enough changes of the parameters of the Hamiltonian, a task that can be hard to achieve near quantum critical points. A powerful alternative is provided by the counterdiabatic modification of the Hamiltonian allowing for an arbitrarily quick implementation of the adiabatic dynamics. Such a counterdiabatic driving protocol has been recently proposed for the quantum Ising model [A. del Campo et al., Phys. Rev. Lett. 109, 115703 (2012)]. We derive an exact closed-form expression for all the coefficients of the counterdiabatic Ising Hamiltonian. We also discuss two approximations to the exact counterdiabatic Ising Hamiltonian quantifying their efficiency of the dynamical preparation of the desired ground state. In particular, these studies show how quantum criticality enhances finite-size effects in the counterdiabatic dynamics.

quant-ph↗
arXiv2014

Numerical studies of ground state fidelity of the Bose-Hubbard model

We compute ground state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the DMRG algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.

cond-mat.str-el↗
arXiv2013

Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field

We derive an exact closed-form expression for fidelity susceptibility of even- and odd-sized quantum Ising chains in the transverse field. To this aim, we diagonalize the Ising Hamiltonian and study the gap between its positive and negative parity subspaces. We derive an exact closed-form expression for the gap and use it to identify the parity of the ground state. We point out misunderstanding in some of the former studies of fidelity susceptibility and discuss its consequences. Last but not least, we rigorously analyze the properties of the gap. For example, we derive analytical expressions showing its exponential dependence on the ratio between the system size and the correlation length.

cond-mat.stat-mech↗
arXiv2012

A quantum phase transition in a quantum external field: Superposing two magnetic phases

We study an Ising chain undergoing a quantum phase transition in a quantum magnetic field. Such a field can be emulated by coupling the chain to a central spin initially in a superposition state. We show that - by adiabatically driving such a system - one can prepare a quantum superposition of any two ground states of the Ising chain. In particular, one can end up with the Ising chain in a superposition of ferromagnetic and paramagnetic phases -- a scenario with no analogue in prior studies of quantum phase transitions. Remarkably, the resulting magnetization of the chain encodes the position of the critical point and universal critical exponents, as well as the ground state fidelity.

quant-ph↗
arXiv2012

On the quantum Coulomb field

The quantum theory of the Coulomb field has been developed by Staruszkiewicz in the long series of papers. This theory explains the universality and quantization of the electric charge observed in Nature. Moreover, the efforts have been made to determine the value of the elementary charge from its mathematical structure. Nonetheless, no other immediate applications of this theory have been proposed. We make such an attempt by (i) considering the classical energy operator and defining its counterpart in the quantum theory of the Coulomb field; (ii) determining the eigenstates of the energy operator and assigning energy to the excitations of the theory; and (iii) proposing a simple theoretical scheme to estimate the effect of the quantum fluctuations of the Coulomb field on the energy levels of hydrogen-like atoms. We argue that the recent experimental advances in hydrogen and muonic-hydrogen spectroscopy may provide the unique window of opportunity for the verification of the Staruszkiewicz's theory.

physics.atom-ph↗
arXiv2011

Scaling of ground state fidelity in the thermodynamic limit: XY model and beyond

We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change of either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is put to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

quant-ph↗
arXiv2011

Critical dynamics of decoherence

We study decoherence induced by a dynamic environment undergoing a quantum phase transition. Environment's susceptibility to perturbations - and, consequently, efficiency of decoherence - is amplified near a critical point. Over and above this near-critical susceptibility increase, we show that decoherence is dramatically enhanced by non-equilibrium critical dynamics of the environment. We derive a simple expression relating decoherence to the universal critical exponents exhibiting deep connections with the theory of topological defect creation in non-equilibrium phase transitions.

quant-ph↗
arXiv2011

Quantum fidelity in the thermodynamic limit

We study quantum fidelity, the overlap between two ground states of a many-body system, focusing on the thermodynamic regime. We show how drop of fidelity near a critical point encodes universal information about a quantum phase transition. Our general scaling results are illustrated in the quantum Ising chain for which a remarkably simple expression for fidelity is found.

quant-ph↗
arXiv2010

Dynamics of a quantum quench in an ultra-cold atomic BCS superfluid

We study dynamics of an ultra-cold atomic BCS superfluid driven towards the BCS superfluid-Fermi liquid quantum critical point by a gradual decrease of the pairing interaction. We analyze how the BCS superfluid falls out of equilibrium and show that the non-equilibrium gap and Cooper pair size reflect critical properties of the transition. We observe three stages of evolution: adiabatic where the Cooper pair size is inversely proportional to the equilibrium gap, weakly non-equilibrium where it is inversely proportional to the non-equilibrium gap, and strongly non-equilibrium where it decouples from both equilibrium and non-equilibrium gap. These phenomena should stimulate future experimental characterization of non-equilibrium ultra-cold atomic BCS superfluids.

cond-mat.quant-gas↗
arXiv2010

Soliton creation during a Bose-Einstein condensation

We use stochastic Gross-Pitaevskii equation to study dynamics of Bose-Einstein condensation. We show that cooling into a Bose-Einstein condensate (BEC) can create solitons with density given by the cooling rate and by the critical exponents of the transition. Thus, counting solitons left in its wake should allow one to determine the critical exponents z and nu for a BEC phase transition. The same information can be extracted from two-point correlation functions.

cond-mat.quant-gas↗
arXiv2009

Quantum phase transition in space in a ferromagnetic spin-1 Bose-Einstein condensate

A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose-Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e., the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent nu.

cond-mat.stat-mech↗
arXiv2008

How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate

We discuss the dynamics of a quantum phase transition in a spin-1 Bose-Einstein condensate when it is driven from the magnetized broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We determine where the condensate goes out of equilibrium as it approaches the critical point, and compute the condensate magnetization at the critical point. This is done within a quantum Kibble-Zurek scheme traditionally employed in the context of symmetry-breaking quantum phase transitions. Then we study the influence of the nonequilibrium dynamics near a critical point on the condensate magnetization. In particular, when the quench stops at the critical point, nonlinear oscillations of magnetization occur. They are characterized by a period and an amplitude that are inversely proportional. If we keep driving the condensate far away from the critical point through the unmagnetized ``symmetric'' polar phase, the amplitude of magnetization oscillations slowly decreases reaching a non-zero asymptotic value. That process is described by the equation that can be mapped onto the classical mechanical problem of a particle moving under the influence of harmonic and ``anti-friction'' forces whose interplay leads to surprisingly simple fixed-amplitude oscillations. We obtain several scaling results relating the condensate magnetization to the quench rate, and verify numerically all analytical predictions.

cond-mat.other↗
arXiv2007

Mott insulator states of ultracold atoms in optical resonators

We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical a.c.-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension, and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.

cond-mat.other↗
arXiv2007

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

cond-mat.other↗