arXiv subjects
Publications and source records attributed to Zbyszek P. Karkuszewski.
All energy measurements of a quantum system are prone to inaccuracies. In particular, if such measurements are carried over a finite period of time the accuracy of the result is affected by the length of that period. Here I show an upper bound on such inaccuracies and point out that the bound can be arbitrarily small if many copies of the system are available.
Here I propose an approximate way of simulating the outcomes of a single-experiment density measurement that is performed on a state of N bosons. The approximation is accurate if occupation of single-particle modes is macroscopic.
The very old problem of extracting frequencies from time signals is addressed in the case of signals that are very short as compared to their intrinsic time scales. The solution of the problem is not only important to the classic signal processing but also helps to disqualify several common formulations of the quantum mechanical time-energy uncertainty principle.
It is impossible to obtain accurate frequencies from time signals of a very short duration. This is a common believe among contemporary physicists. Here I present a practical way of extracting energies to a high precision from very short time signals produced by a quantum system. The product of time span of the signal and the precision of found energies is well bellow the limit imposed by the time-energy uncertainty relation.
The dark soliton created in a Bose-Einstein condensate becomes grey in course of time evolution because its notch fills up with depleted atoms. This is the result of quantum mechanical calculations which describes output of many experimental repetitions of creation of the stationary soliton, and its time evolution terminated by a destructive density measurement. However, such a description is not suitable to predict the outcome of a single realization of the experiment were two extreme scenarios and many combinations thereof are possible: one will see (1) a displaced dark soliton without any atoms in the notch, but with a randomly displaced position, or (2) a grey soliton with a fixed position, but a random number of atoms filling its notch. In either case the average over many realizations will reproduce the mentioned quantum mechanical result. In this paper we use N-particle wavefunctions, which follow from the number-conserving Bogoliubov theory, to settle this issue.
We study a Bose-Einstein condensate trapped in an asymmetric double well potential. Solutions of the time-independent Gross-Pitaevskii equation reveal intrinsic loops in the energy (or chemical potential) level behavior when the shape of the potential is varied. We investigate the corresponding behavior of the quantum (many-body) energy levels. Applying the two-mode approximation to the bosonic field operators, we show that the quantum energy levels create an anti-crossing net inside the region bounded by the loop of the mean field solution.
We analyze greying of the dark soliton in a Bose-Einstein condensate in the limit of weak interaction between atoms. The condensate initially prepared in the excited dark soliton state is loosing atoms because of spontaneous quantum depletion. These atoms are depleted from the soliton state into single particle states with nonzero density in the notch of the soliton. As a result the image of the soliton is losing contrast. This quantum depletion mechanism is efficient even at zero temperature when a thermal cloud is absent.
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to decoherence in situations when the environment has a chaotic classical counterpart.
An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.
Breakdown of quantum-classical correspondence is studied on an experimentally realizable example of one-dimensional periodically driven system. Two relevant time scales are identified in this system: the short Ehrenfest time t_h and the typically much longer localization time scale T_L. It is shown that surprisingly weak modification of the Hamiltonian may eliminate the more dramatic symptoms of localization without effecting the more subtle but ubiquitous and rapid loss of correspondence at t_h.
It is shown that by an appropriate modification of the trapping potential one may create collective excitation in cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally --- it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.