Phase-intensity uncertainty relation from quasiprobability distributions

Orłowski, Arkadiusz; Paul, H.; Böhmer, B.

doi:10.1016/s0030-4018(97)00086-2

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…Further discussion on entropic uncertainty relations associated with the phase-number uncertainties can be found in Ref. [69].…”

Section: St àHlnmentioning

confidence: 99%

Uncertainty, Entropy and Decoherence of the Damped Harmonic Oscillator in the Lindblad Theory of Open Quantum Systems

Исар

1999

Fortschr. Phys.

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In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a Wigner distribution function which is Gaussian in form is found to depend only on the variance of the distribution function. We give a series of inequalities, relating uncertainty to von Neumann entropy and linear entropy. We analyze the conditions for purity of states and show that for a special choice of the diffusion coefficients, the correlated coherent states (squeezed coherent states) are the only states which remain pure all the time during the evolution of the considered system. These states are also the most stable under evolution in the presence of the environment and play an important role in the description of environment induced decoherence.

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“…Further discussion on entropic uncertainty relations associated with the phase-number uncertainties can be found in Ref. [69].…”

Section: St àHlnmentioning

confidence: 99%

Uncertainty, Entropy and Decoherence of the Damped Harmonic Oscillator in the Lindblad Theory of Open Quantum Systems

Исар

1999

Fortschr. Phys.

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“…The vacuum state, and similarly coherent (or displaced vacuum) states, are minimum uncertainty states in which † The predicted strain (DL/L) on the detector arms is of the order 10 20 [118] . ‡ Formailsing this discussion is non-trivial due to difficulties in defining a proper phase operator (strictly a Hermitian phase operator can only be defined for a finite-dimensional Hilbert space [120] ). For the purposes of this discussion it is sufficient to note that intensity and phase are canonically conjugate variables.…”

Section: Ligo: a Case Study In The Application Of Correlated Particlesmentioning

confidence: 99%

Non-equilibrium dynamics of Bose Einstein condensates

Mills¹

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This thesis examines two aspects of the non-equilibrium dynamics of Bose-Einstein condensates (BECs). Our particular interests are the relaxation of near-integrable systems, and the inter-particle correlations present in BECs, both in equilibrium and following an abrupt change in the Hamiltonian.In the first part of this thesis we investigate the stability of solitary wave solutions to a system of two coupled one-dimensional non-linear Schrödinger equations (CNLSE). This system has an integrable point known as the Manakov [1] model which has analytic dark-bright soliton solutions [2] . We break the integrability of this model by varying the inter-species interaction strength, and employ variational and numerical methods in order to find dark-bright solitary wave solutions, away from the integrable point.The time evolution of these states is calculated via numerical integration of the CNLSE, which allows us to assess the stability of these solutions in isolation and to quantify their robustness against collisions with a dark soliton. We find that there is a broad region of the parameter space in which solutions for black-bright (stationary) solitary waves can be found. In this domain, the integrability breaking is revealed only during collisions. Prior to a collision, the numerical solutions are indistinguishable from true solitons, however, the collisional stability of these solitary waves is significantly affected by the extent to which integrability is broken. We find that there is a smooth transition between the non-dispersive particle-like nature of soliton interactions for integrable systems, and the destructive collisions which take place when the system is perturbed far from the integrable point.In the case of moving (grey-bright) solitary waves, we find a more restricted region of the parameter space which admits solitary wave solutions. In this domain we are able to find approximately stable solitary wave solutions using a variational ansatz. The collisional stability of these grey-bright solitary waves is also found to depend upon the extent to which integrability is broken.We conclude that the observation of stable, long-lived dark-bright solitary waves is not sufficient to indicate near-integrability of the two-component system. However, near-integrability may inferred if dark-bright solitary waves are observed to survive multiple collisions. These results are not only of theoretical interest, but may also inform future experiments which explore the behaviour of solitary waves in two-component Bose-Einstein condensates.Following this we investigate the properties of magnetic solitary wave solutions to the CNLSE. We find that the analytic 'magnetic soliton' solutions derived in reference [3] are dynamically unstable and relax to non-stationary magnetic solitary wave states over a short timescale. We investigate the collisional dynamics of these magnetic solitary waves and find that these excitations are remarkably robust.In the second part of this thesis we calculate the fluctuations in the nu...

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Complementarity and duality relations for finite-dimensional systems

Luis

2003

Phys. Rev. A

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We generalize to systems with arbitrary finite dimension a measure of quantum fluctuations ͑the certainty͒ previously introduced for two-dimensional systems. Using this measure, we study the duality relations satisfied by complementary observables looking for states with minimum joint fluctuations ͑maximum certainty states͒. We extend the duality relations to encompass several complementary observables simultaneously.

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Phase-intensity uncertainty relation from quasiprobability distributions

Cited by 3 publications

References 21 publications

Uncertainty, Entropy and Decoherence of the Damped Harmonic Oscillator in the Lindblad Theory of Open Quantum Systems

Uncertainty, Entropy and Decoherence of the Damped Harmonic Oscillator in the Lindblad Theory of Open Quantum Systems

Non-equilibrium dynamics of Bose Einstein condensates

Complementarity and duality relations for finite-dimensional systems

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