S.V. Lawande

Exact steady-state density operator for a collective atomic system in an external field

Abstract An exact steady-state density operator is obtained for a model describing the collective behaviour of a system of N two-level atoms driven by a classical field. This is used to obtain the exact steady-state expectation value of the atomic population difference for any N .

Feynman propagator for the δ-function potential

Abstract A new derivation of the Feynman propagator for the Dirac δ-function potential is presented.

Intensity fluctuations in a driven Dicke model

Exact analytic results for the steady-state atomic correlation functions of arbitrary order n are given for a system of N superimposed two-level atoms (the Dicke model) collectively interacting with an imposed C.W. laser field. Photon statistical studies through the normalised intensity-intensity correlation function, g(2)(0), show that when both N and the driving field become large, g(2)(0) → 1.2. This compares with an earlier approximated calculation1) which allows an independent atomic decay mechanism giving rise to g(2)(0) ≈ 2. Cooperative interactions thus reduce intensity fluctuations. Photon anti-bunching occurs for finite N. There is a second-order phase transition critical bifurcation point in a thermodynamic limit in which N → ∞; a critical exponent is determined.

Non-resonant effects in the fluorescent Dicke model. I. Exact steady state analysis

The exact steady state solution for the reduced atomic density operator for a model of N identical two-level atoms occupying the same site (the Dicke model) and driven by a CW off-resonant laser field is presented. Exact expressions are given for the atomic observables and atomic correlation functions of arbitrary order. Exact thermodynamic analysis (N to infinity ) shows that the critical phase transition behaviour found in the resonant case is destroyed due to non-resonant effects. For large N and increasing detuning parameter, quantum fluctuations tend to vanish and hence the atomic observables tend to assume their semiclassical values. Also it is found that for a fixed arbitrary detuning parameter and increasing N these fluctuations disappear for the whole range of the driving field strength. The authors explain why it is not possible in the limit N to infinity to recover the correct asymptotic limit for the resonant case from the results of the dispersive case.

Time-dependent invariants and stable coherent states

Abstract The time evolution of a coherent state is discussed using an explicitly time-dependent invariant of the underlying hamiltonian. It is shown that a stable coherent state is an eigenstate of such an invariant.

Dispersion in the driven dicke model

Abstract An exact steady state solution for the atomic density operator is obtained for a model of N identical superimposed two- level atoms (the Dicke model) driven by a cw off-resonance laser field. Exact expressions are given then for the atomic observables and their fluctuations and for the atomic correlation functions for any N. The results show that the second order phase transition critical bifurcation point found in the resonant case and for N → ∞ disappears due to the dispersive (non- resonant) effects. This is confirmed, further, by an exact semiclassical analysis of the governing equations of motion.

On exact master equation for an open system

Abstract An exact equation is obtained for the evolution of density matrix in the coherent state representation for the open system of a single harmonic oscillator coupled to a reservoir of N oscillators.

Path integration of a quadratic action with a generalized memory

Abstract Path integration of an action representing a harmonic oscillator with a generalized memory is carried out within the framework of Feynmans polygonal approach. The exact propagator obtained is in the form of an exponential integral over a single variable. Closed analytical results are available for special cases of the memory function.

Exact thermodynamic behaviour of a collective atomic system in an external field

An exact steady-state density operator is obtained for a model describing the collective behaviour of a system of N two-level atoms. The model yields a Fokker-Planck equation which does not satisfy detailed balance. The density operator is further employed to obtain exact analytical expressions for steady-state expectation values of the collective atomic operators both for finite N and in the thermodynamic limit N → ∞.

Exact analysis of the critical behaviour in the driven Dicke model of interacting atoms

A system of N identical two-level atoms occupying the same site (the Dicke model) interacting with one another and driven by a coherent field is considered. From the known exact steady-state atomic density operator, expressions for the atomic observables, their fluctuations and correlation functions are constructed. Asymptotic analysis is used to obtain the behaviour of these atomic variables with respect to the parameters of the driving field in the thermodynamic limit N → ∞. It is shown that the interplay between the parameters of the interatomic interactions and the driving field leads to a critical behaviour as N → ∞. The conditions under which the atomic system shows either a first order or a second order phase transition with respect to the field variables are discussed.