5,774 research outputs found
Stochastic mean-field dynamics for fermions in the weak coupling limit
Assuming that the effect of the residual interaction beyond mean-field is
weak and has a short memory time, two approximate treatments of correlation in
fermionic systems by means of Markovian quantum jump are presented. A
simplified scenario for the introduction of fluctuations beyond mean-field is
first presented. In this theory, part of the quantum correlations between the
residual interaction and the one-body density matrix are neglected and jumps
occur between many-body densities formed of pairs of states where and are
antisymmetrized products of single-particle states. The underlying Stochastic
Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a
spherical Ca nucleus under the influence of a statistical ensemble of
two-body contact interaction. This framework is however too simplistic to
account for both fluctuation and dissipation. In the second part of this work,
an alternative quantum jump method is obtained without making the approximation
on quantum correlations. Restricting to two particles-two holes residual
interaction, the evolution of the one-body density matrix of a correlated
system is transformed into a Lindblad equation. The associated dissipative
dynamics can be simulated by quantum jumps between densities written as is a normalized Slater determinant. The
associated stochastic Schroedinger equation for single-particle wave-functions
is given.Comment: Enlarged version, 10 pages, 2 figure
Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids
A controlled hybridization between full quantum dynamics and semiclassical
approaches (mean-field and truncated Wigner) is implemented for interacting
many-boson systems. It is then demonstrated how simulating the resulting hybrid
evolution equations allows one to obtain the full quantum dynamics for much
longer times than is possible using an exact treatment directly. A collision of
sodium BECs with 1.x10^5 atoms is simulated, in a regime that is difficult to
describe semiclassically. The uncertainty of physical quantities depends on the
statistics of the full quantum prediction. Cutoffs are minimised to a
discretization of the Hamiltonian. The technique presented is quite general and
extension to other systems is considered.Comment: Published version. Broader background and discussion, slightly
shortened, less figures in epaps. Research part unchanged. Article + epaps
(4+4 pages), 8 figure
Bogoliubov dynamics of condensate collisions using the positive-P representation
We formulate the time-dependent Bogoliubov dynamics of colliding
Bose-Einstein condensates in terms of a positive-P representation of the
Bogoliubov field. We obtain stochastic evolution equations for the field which
converge to the full Bogoliubov description as the number of realisations
grows. The numerical effort grows linearly with the size of the computational
lattice. We benchmark the efficiency and accuracy of our description against
Wigner distribution and exact positive-P methods. We consider its regime of
applicability, and show that it is the most efficient method in the common
situation - when the total particle number in the system is insufficient for a
truncated Wigner treatment.Comment: 9 pages. 5 figure
Quantum feedback cooling of a single trapped ion in front of a mirror
We develop a theory of quantum feedback cooling of a single ion trapped in
front of a mirror. By monitoring the motional sidebands of the light emitted
into the mirror mode we infer the position of the ion, and act back with an
appropriate force to cool the ion. We derive a feedback master equation along
the lines of the quantum feedback theory developed by Wiseman and Milburn,
which provides us with cooling times and final temperatures as a function of
feedback gain and various system parameters.Comment: 15 pages, 11 Figure
Irreversible photon transfer in an ensemble of -type atoms and photon diode
We show that a pair of quantized cavity modes interacting with a spectrally
broadened ensemble of Lambda-type atoms is analogous to an ensemble of two
level systems coupled to a bosonic reservoir. This provides the possibility for
an irreversible photon transfer between photon modes. The density of states as
well as the quantum state of the reservoir can be engineered allowing the
observation of effects such as the quantum Zeno- and anti-Zeno effect, the
destructive interference of decay channels and the decay in a squeezed vacuum.
As a particular application we discuss a photon diode, i.e. a device which
directs a single photon from anyone of two input ports to a common output port.Comment: 5 pages, 2 figure
Quantum turbulence and correlations in Bose-Einstein condensate collisions
We investigate numerically simulated collisions between experimentally
realistic Bose-Einstein condensate wavepackets, within a regime where highly
populated scattering haloes are formed. The theoretical basis for this work is
the truncated Wigner method, for which we present a detailed derivation, paying
particular attention to its validity regime for colliding condensates. This
paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and
C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)] and we investigate both
single-trajectory solutions, which reveal the presence of quantum turbulence in
the scattering halo, and ensembles of trajectories, which we use to calculate
quantum-mechanical correlation functions of the field
Optomechanical trapping and cooling of partially transparent mirrors
We consider the radiative trapping and cooling of a partially transmitting
mirror suspended inside an optical cavity, generalizing the case of a perfectly
reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys.
Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in
an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.},
arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system
depend strongly on the position of the middle mirror, leading to important
qualitative differences in the radiation pressure effects: in one case, the
situation is similar that of a perfectly reflecting middle mirror, with only
minor quantitative modifications. In addition, we also identify a range of
mirror positions for which the radiation-mirror coupling becomes purely
dispersive and the back-action effects that usually lead to cooling are absent,
although the mirror can still be optically trapped. The existence of these two
regimes leads us to propose a bichromatic scheme that optimizes the cooling and
trapping of partially transmissive mirrors.Comment: Submitted to Phys.Rev.
PT-symmetric quantum Liouvillian dynamics
We discuss a combination of unitary and anti-unitary symmetry of quantum
Liouvillian dynamics, in the context of open quantum systems, which implies a
D2 symmetry of the complex Liovillean spectrum. For sufficiently weak
system-bath coupling it implies a uniform decay rate for all coherences, i.e.
off-diagonal elements of the system's density matrix taken in the eigenbasis of
the Hamiltonian. As an example we discuss symmetrically boundary driven open
XXZ spin 1/2 chains.Comment: Note [18] added with respect to a published version, explaining the
symmetry of the matrix V [eq. (14)
Emergent classicality in continuous quantum measurements
We develop a classical theoretical description for nonlinear many-body
dynamics that incorporates the back-action of a continuous measurement process.
The classical approach is compared with the exact quantum solution in an
example with an atomic Bose-Einstein condensate in a double-well potential
where the atom numbers in both potential wells are monitored by light
scattering. In the classical description the back-action of the measurements
appears as diffusion of the relative phase of the condensates on each side of
the trap. When the measurements are frequent enough to resolve the system
dynamics, the system behaves classically. This happens even deep in the quantum
regime, and demonstrates how classical physics emerges from quantum mechanics
as a result of measurement back-action
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
We show that the dynamics of interacting fermions can be exactly replaced by
a quantum jump theory in the many-body density matrix space. In this theory,
jumps occur between densities formed of pairs of Slater determinants, , where each state evolves according to the Stochastic
Schr\"odinger Equation (SSE) given in ref. \cite{Jul02}. A stochastic
Liouville-von Neumann equation is derived as well as the associated
Bogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form
of the many-body density along the path, the presented theory is equivalent to
a stochastic theory in one-body density matrix space, in which each density
matrix evolves according to its own mean field augmented by a one-body noise.
Guided by the exact reformulation, a stochastic mean field dynamics valid in
the weak coupling approximation is proposed. This theory leads to an
approximate treatment of two-body effects similar to the extended
Time-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean
field dynamics, statistical mixing can be directly considered and jumps occur
on a coarse-grained time scale. Accordingly, numerical effort is expected to be
significantly reduced for applications.Comment: 12 pages, 1 figur
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