arXiv subjects

S. Lakshmibala

Publications and source records attributed to S. Lakshmibala.

32 records · Page 2Linked to original sources

arXiv2014

Dynamics of an open quantum system interacting with a quantum environment

We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The Mandel $Q$ parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).

quant-ph↗

arXiv2009

Recurrence properties of quantum observables in wave packet dynamics

We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time distributions, return maps and recurrence plots, we conclude that the dynamics of appropriate observables pertaining to the field can vary from quasiperiodicity to hyperbolicity, depending on the extent of the nonlinearity and of the departure from coherence of the initial state of the field. We establish that, in a simple bipartite model in which the field is effectively an open quantum system, a decaying exponential recurrence-time distribution, characteristic of a hyperbolic dynamical system, is associated with chaotic temporal evolution as characterized by a positive Liapunov exponent.

quant-ph↗

arXiv2007

Ergodicity properties of quantum expectation values in entangled states

Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics of the total system is regular. The time series of the mean photon number is studied over a range of values of the ratio of the strength $γ$ of the nonlinearity to that of the inter-mode coupling $g$. We obtain the power spectrum, estimate the embedding dimension of the reconstructed phase space and the maximal Liapunov exponent $λ_{\rm max}$, and find the recurrence-time distribution of the coarse-grained dynamics. The dynamical behavior ranges from quasiperiodicity (for $γ/g \ll 1$) to chaos as characterized by $λ_{\rm max} > 0$ (for $γ/g \gtrsim 1$), and is interpreted.

quant-ph↗

arXiv2006

Wave packet dynamics of entangled two-mode states

We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state, or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ``overlap fidelity'' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher-order squeezing.

quant-ph↗

arXiv2005

Non-classical properties of quantum wave packets propagating in a Kerr-like medium

We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.

quant-ph↗

arXiv2004

Wave packet dynamics of the matter wave field of a Bose-Einstein condensate

We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of the matter wave field in a Bose-Einstein condensate, or of a suitably chosen initial state of the radiation field propagating in a Kerr-like medium.

quant-ph↗

arXiv2004

Signatures of wave packet revival phenomena in the expectation values of observables

Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially coherent wave packet in a Kerr-like medium), it is shown that distinctive signatures of these revivals and fractional revivals are displayed by the time evolution of the expectation values of physical observables and their powers, i.e., by experimentally measurable quantities. Moreover, different fractional revivals can be selectively identified by examining appropriate higher moments.

quant-ph↗

arXiv2002

Gauge Theoretic Chaology

We review here the work done on the occurence of chaotic configurations in systems derived from Gauge theories. These include Yang-Mills and associated field theories with modifications including Chern Simons and Higgs fields.

hep-th↗

arXiv1999

Quantum revivals, geometric phases and circle map recurrences

Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincaré recurrences for a rotation map: only three distinct revival times can occur, with specified weights. A link is thus established between quantum revivals and recurrences in a coarse-grained discrete-time dynamical system.

quant-ph↗

arXiv1999

Control of Wave Packet Revivals Using Geometric Phases

Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that the latter can be eliminated by inducing suitable geometric phases in the states, by varying the parameters in the Hamiltonian cyclically with a period T. Further, with the introduction of this natural time step T, the occurrence of near revivals can be mapped onto that of Poincaré recurrences in an irrational rotation map of the circle. The distinctive recurrence time statistics of the latter can thus serve as a clear signature of the dynamics of wave packet revivals.

quant-ph↗

arXiv1999

Ladder operators for isospectral oscillators

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.

quant-ph↗

arXiv1999

Geometric phases for generalized squeezed coherent states

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.

quant-ph↗

arXiv1999

Noise-amplitude dependence of the invariant density for noisy, fully chaotic one-dimensional maps

We present some analytic, non-perturbative results for the invariant density rho(x) for noisy one-dimensional maps at fully developed chaos. Under periodic boundary conditions, the Fourier expansion method is used to show precisely how noise makes rho(x) absolutely continuous and smoothens it out. Simple solvable models are used to illustrate the explicit dependence of rho(x) on the amplitude eta of the noise distribution, all the way from the case of zero noise (eta > 0) to the completely noise-dominated limit (eta=1).

chao-dyn↗

arXiv1996

Order-chaos transitions in field theories with topological terms: a dynamical systems approach

We present a comparative study of the dynamical behaviour of topological systems of recent interest, namely the non-Abelian Chern-Simons Higgs system and the Yang-Mills Chern-Simons Higgs system. By reducing the full field theories to temporal differential systems using the assumption of spatially homogeneous fields , we study the Lyapunov exponents for two types of initial conditions. We also examine in minute detail the behaviour of the Lyapunov spectra as a function of the various coupling parameters in the system. We compare and contrast our results with those for Abelian Higgs, Yang-Mills Higgs and Yang-Mills Chern-Simons systems which have been discussed by other authors recently. The role of the various terms in the Hamiltonians for such systems in determining the order-disorder transitions is emphasized and shown to be counter-intuitive in the Yang-Mills Chern-Simons Higgs systems.

hep-th↗