862 research outputs found
Universal state inversion and concurrence in arbitrary dimensions
Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for
the entanglement of formation of two qubits in terms of what he calls the
concurrence of the joint density operator. Wootters's concurrence is defined
with the help of the superoperator that flips the spin of a qubit. We
generalize the spin-flip superoperator to a "universal inverter," which acts on
quantum systems of arbitrary dimension, and we introduce the corresponding
concurrence for joint pure states of (D1 X D2) bipartite quantum systems. The
universal inverter, which is a positive, but not completely positive
superoperator, is closely related to the completely positive universal-NOT
superoperator, the quantum analogue of a classical NOT gate. We present a
physical realization of the universal-NOT superoperator.Comment: Revtex, 25 page
Quasienergy description of the driven Jaynes-Cummings model
We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a
quasienergy approach by switching to a frame rotating with the external
modulation frequency and by using the dressed atom picture. A quasienergy
surface in phase space emerges whose level spacing is governed by a rescaled
effective Planck constant. Moreover, the well-known multiphoton transitions can
be reinterpreted as resonant tunneling transitions from the local maximum of
the quasienergy surface. Most importantly, the driving defines a quasienergy
well which is nonperturbative in nature. The quantum mechanical quasienergy
state localized at its bottom is squeezed. In the Purcell limited regime, the
potential well is metastable and the effective local temperature close to its
minimum is uniquely determined by the squeezing factor. The activation occurs
in this case via dressed spin flip transitions rather than via quantum
activation as in other driven nonlinear quantum systems such as the quantum
Duffing oscillator. The local maximum is in general stable. However, in
presence of resonant coherent or dissipative tunneling transitions the system
can escape from it and a stationary state arises as a statistical mixture of
quasienergy states being localized in the two basins of attraction. This gives
rise to a resonant or an antiresonant nonlinear response of the cavity at
multiphoton transitions. The model finds direct application in recent
experiments with a driven superconducting circuit QED setup.Comment: 13 pages, 8 fi
Standard Quantum Limits for broadband position measurement
I utilize the Caves-Milburn model for continuous position measurements to
formulate a broadband version of the Standard Quantum Limit (SQL) for
monitoring the position of a free mass, and illustrate the use of Kalman
filtering to recover the SQL for estimating a weak classical force that acts on
a quantum-mechanical test particle under continuous observation. These
derivations are intended to clarify the interpretation of SQL's in the context
of continuous quantum measurement.Comment: Replaced version: changed title, fixed algebra error at the very end,
conclusions modified accordingly. Four pages, one eps figur
Wave packet dynamics of entangled two-mode states
We consider a model Hamiltonian describing the interaction of a single-mode
radiation field with the atoms of a nonlinear medium, and study the dynamics of
entanglement for specific non-entangled initial states of interest: namely,
those in which the field mode is initially in a Fock state, a coherent state,
or a photon-added coherent state. The counterparts of near-revivals and
fractional revivals are shown to be clearly identifiable in the entropy of
entanglement. The ``overlap fidelity'' of the system is another such indicator,
and its behaviour corroborates that of the entropy of entanglement in the
vicinity of near-revivals. The expectation values and higher moments of
suitable quadrature variables are also examined, with reference to possible
squeezing and higher-order squeezing.Comment: 18 pages, 7 figure
Analytic Approximation of the Tavis-Cummings Ground State via Projected States
We show that an excellent approximation to the exact quantum solution of the
ground state of the Tavis-Cummings model is obtained by means of a
semi-classical projected state. This state has an analytical form in terms of
the model parameters and, in contrast to the exact quantum state, it allows for
an analytical calculation of the expectation values of field and matter
observables, entanglement entropy between field and matter, squeezing
parameter, and population probability distributions. The fidelity between this
projected state and the exact quantum ground state is very close to 1, except
for the region of classical phase transitions. We compare the analytical
results with those of the exact solution obtained through the direct
Hamiltonian diagonalization as a function of the atomic separation energy and
the matter-field coupling.Comment: 22 pages, 13 figures, accepted for publication in Physics Script
Scalable quantum field simulations of conditioned systems
We demonstrate a technique for performing stochastic simulations of
conditional master equations. The method is scalable for many quantum-field
problems and therefore allows first-principles simulations of multimode bosonic
fields undergoing continuous measurement, such as those controlled by
measurement-based feedback. As examples, we demonstrate a 53-fold speed
increase for the simulation of the feedback cooling of a single trapped
particle, and the feedback cooling of a quantum field with 32 modes, which
would be impractical using previous brute force methods.Comment: 5 pages, 2 figure
Quantum Coherence and Classical Chaos in a Pulsed Parametric Oscillator with a Kerr Nonlinearity
We consider a parametric amplifier driven by a periodically pulsed pump field inside a cavity containing a Kerr nonlinearity. The dynamics of the device is modeled as a kicked nonlinear system. The pulsed parametric amplifier constitutes the kick. In between kicks the dynamics is determined by the Kerr nonlinearity and damping. In the absence of damping, a classical description of the device exhibits a rich phase-space structure including fixed points of multiple period and chaos. We contrast the classical behavior of the mean intensity with that predicted by quantum dynamics. The mean photon number inside the cavity is shown to undergo regular collapse and revival in the regular region of the phase space and irregular revivals in the chaotic region. When damping is included, the quantum recurrences are rapidly suppressed, and the classical behavior is restored. In this case a stable steady state is possible. The damping represents the effect of photon-number measurements on the system. We also discuss the photon statistics in the steady state
Schrodinger cats and their power for quantum information processing
We outline a toolbox comprised of passive optical elements, single photon
detection and superpositions of coherent states (Schrodinger cat states). Such
a toolbox is a powerful collection of primitives for quantum information
processing tasks. We illustrate its use by outlining a proposal for universal
quantum computation. We utilize this toolbox for quantum metrology
applications, for instance weak force measurements and precise phase
estimation. We show in both these cases that a sensitivity at the Heisenberg
limit is achievable.Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on
"Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus
Memorial Issue
The dynamics of a strongly driven two component Bose-Einstein Condensate
We consider a two component Bose-Einstein condensate in two spatially
localized modes of a double well potential, with periodic modulation of the
tunnel coupling between the two modes. We treat the driven quantum field using
a two mode expansion and define the quantum dynamics in terms of the Floquet
Operator for the time periodic Hamiltonian of the system. It has been shown
that the corresponding semiclassical mean-field dynamics can exhibit regions of
regular and chaotic motion. We show here that the quantum dynamics can exhibit
dynamical tunneling between regions of regular motion, centered on fixed points
(resonances) of the semiclassical dynamics
Deformed versus undeformed cat states encoding qubit
We study the possibility of exploiting superpositions of coherent states to
encode qubit. A comparison between the use of deformed and undeformed bosonic
algebra is made in connection with the amplitude damping errors.Comment: 6 pages, 2 eps figures, to appear in J. Opt.
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