3,010 research outputs found
The three-site Bose-Hubbard model subject to atom losses: the boson-pair dissipation channel and failure of the mean-field approach
We employ the perturbation series expansion for derivation of the reduced
master equations for the three-site Bose-Hubbard model subject to strong atom
losses from the central site. The model describes a condensate trapped in a
triple-well potential subject to externally controlled removal of atoms. We
find that the -phase state of the coherent superposition between the side
wells decays via two dissipation channels, the single-boson channel (similar to
the externally applied dissipation) and the boson-pair channel. The quantum
derivation is compared to the classical adiabatic elimination within the
mean-field approximation. We find that the boson-pair dissipation channel is
not captured by the mean-field model, whereas the single-boson channel is
described by it. Moreover, there is a matching condition between the zero-point
energy bias of the side wells and the nonlinear interaction parameter which
separates the regions where either the single-boson or the boson-pair
dissipation channel dominate. Our results indicate that the -site
Bose-Hubbard models, for , subject to atom losses may require an analysis
which goes beyond the usual mean-field approximation for correct description of
their dissipative features. This is an important result in view of the recent
experimental works on the single site addressability of condensates trapped in
optical lattices.Comment: 9 pages; 3 figures in color; submitted to PR
Effect of atomic beam alignment on photon correlation measurements in cavity QED
Quantum trajectory simulations of a cavity QED system comprising an atomic
beam traversing a standing-wave cavity are carried out. The delayed photon
coincident rate for forwards scattering is computed and compared with the
measurements of Rempe et al. [Phys. Rev. Lett. 67, 1727 (1991)] and Foster et
al. [Phys. Rev. A 61, 053821 (2000)]. It is shown that a moderate atomic beam
misalignment can account for the degradation of the predicted correlation. Fits
to the experimental data are made in the weak-field limit with a single
adjustable parameter--the atomic beam tilt from perpendicular to the cavity
axis. Departures of the measurement conditions from the weak-field limit are
discussed.Comment: 15 pages and 13 figure
Non-classical photon pair generation in atomic vapours
A scheme for the generation of non-classical pairs of photons in atomic
vapours is proposed. The scheme exploits the fact that the cross correlation of
the emission of photons from the extreme transitions of a four-level cascade
system shows anti-bunching which has not been reported earlier and which is
unlike the case of the three level cascade emission which shows bunching. The
Cauchy-Schwarz inequality which is the ratio of cross-correlation to the auto
correlation function in this case is estimated to be for
controllable time delay, and is one to four orders of magnitude larger compared
to previous experiments. The choice of Doppler free geometry in addition to the
fact that at three photon resonance the excitation/deexcitation processes occur
in a very narrow frequency band, ensures cleaner signals.Comment: 18 pages, 7 figure
Non-Markovian Quantum Trajectories Versus Master Equations: Finite Temperature Heat Bath
The interrelationship between the non-Markovian stochastic Schr\"odinger
equations and the corresponding non-Markovian master equations is investigated
in the finite temperature regimes. We show that the general finite temperature
non-Markovian trajectories can be used to derive the corresponding
non-Markovian master equations. A simple, yet important solvable example is the
well-known damped harmonic oscillator model in which a harmonic oscillator is
coupled to a finite temperature reservoir in the rotating wave approximation.
The exact convolutionless master equation for the damped harmonic oscillator is
obtained by averaging the quantum trajectories relying upon no assumption of
coupling strength or time scale. The master equation derived in this way
automatically preserves the positivity, Hermiticity and unity.Comment: 19 pages, typos corrected, references adde
Preparation information and optimal decompositions for mixed quantum states
Consider a joint quantum state of a system and its environment. A measurement
on the environment induces a decomposition of the system state. Using
algorithmic information theory, we define the preparation information of a pure
or mixed state in a given decomposition. We then define an optimal
decomposition as a decomposition for which the average preparation information
is minimal. The average preparation information for an optimal decomposition
characterizes the system-environment correlations. We discuss properties and
applications of the concepts introduced above and give several examples.Comment: 13 pages, latex, 2 postscript figure
Non-linear emission spectra of quantum dots strongly coupled to photonic mode
A theory of optical emission of quantum dot arrays in quantum microcavities
is developed. The regime of the strong coupling between the quantum dots and
photonic mode of the cavity is considered. The quantum dots are modeled as
two-level systems. In the low pumping (linear) regime the emission spectra are
mainly determined by the superradiant mode where the effective dipoles of the
dots oscillate in phase. In the non-linear regime the superradiant mode is
destroyed and the emission spectra are sensitive to the parity of quantum dot
number. Further increase of the pumping results in the line width narrowing
being an evidence of the lasing regime.Comment: 11 pages, 6 figure
Undoing a weak quantum measurement of a solid-state qubit
We propose an experiment which demonstrates the undoing of a weak continuous
measurement of a solid-state qubit, so that any unknown initial state is fully
restored. The undoing procedure has only a finite probability of success
because of the non-unitary nature of quantum measurement, though it is
accompanied by a clear experimental indication of whether or not the undoing
has been successful. The probability of success decreases with increasing
strength of the measurement, reaching zero for a traditional projective
measurement. Measurement undoing (``quantum un-demolition'') may be interpreted
as a kind of a quantum eraser, in which the information obtained from the first
measurement is erased by the second measurement, which is an essential part of
the undoing procedure. The experiment can be realized using quantum dot
(charge) or superconducting (phase) qubits.Comment: 5 page
Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
Stochastic Schr{\"o}dinger equations for quantum trajectories offer an
alternative and sometimes superior approach to the study of open quantum system
dynamics. Here we show that recently established convolutionless non-Markovian
stochastic Schr{\"o}dinger equations may serve as a powerful tool for the
derivation of convolutionless master equations for non-Markovian open quantum
systems. The most interesting example is quantum Brownian motion (QBM) of a
harmonic oscillator coupled to a heat bath of oscillators, one of the
most-employed exactly soluble models of open system dynamics. We show
explicitly how to establish the direct connection between the exact
convolutionless master equation of QBM and the corresponding convolutionless
exact stochastic Schr\"odinger equation.Comment: 18 pages, RevTe
Entangled-State Cycles of Atomic Collective-Spin States
We study quantum trajectories of collective atomic spin states of
effective two-level atoms driven with laser and cavity fields. We show that
interesting ``entangled-state cycles'' arise probabilistically when the (Raman)
transition rates between the two atomic levels are set equal. For odd (even)
, there are () possible cycles. During each cycle the
-qubit state switches, with each cavity photon emission, between the states
, where is a Dicke state in a rotated
collective basis. The quantum number (), which distinguishes the
particular cycle, is determined by the photon counting record and varies
randomly from one trajectory to the next. For even it is also possible,
under the same conditions, to prepare probabilistically (but in steady state)
the Dicke state , i.e., an -qubit state with excitations,
which is of particular interest in the context of multipartite entanglement.Comment: 10 pages, 9 figure
Emergence of classicality in small number entangled systems
We show the transition from a fully quantized interaction to a semiclassical
one in entangled small number quantum systems using the quantum trajectories
approach. In particular, we simulate the microwave Ramsey zones used in Rydberg
atom interferometry, filling in the gap between the strongly entangling Jaynes
Cummings evolution and the semiclassical rotation of the atomic internal
states. We also correlate the information flowing with leaking photons to the
entanglement generation between cavity field and flying atom and detail the
roles played by the strong dissipation and the external driving force in
preserving atomic coherence through the interaction.Comment: 4 pages, 6 figure
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