5,531 research outputs found
Quantum trajectories for propagating Fock states
We derive quantum trajectories (also known as stochastic master equations)
that describe an arbitrary quantum system probed by a propagating wave packet
of light prepared in a continuous-mode Fock state. We consider three detection
schemes of the output light: photon counting, homodyne detection, and
heterodyne detection. We generalize to input field states that are
superpositions and or mixtures of Fock states and illustrate the formalism with
several examples.Comment: 20 pages, 4 figure
Collective Uncertainty in Partially-Polarized and Partially-Decohered Spin-1/2 Systems
It has become common practice to model large spin ensembles as an effective
pseudospin with total angular momentum J = N x j, where j is the spin per
particle. Such approaches (at least implicitly) restrict the quantum state of
the ensemble to the so-called symmetric Hilbert space. Here, we argue that
symmetric states are not generally well-preserved under the type of decoherence
typical of experiments involving large clouds of atoms or ions. In particular,
symmetric states are rapidly degraded under models of decoherence that act
identically but locally on the different members of the ensemble. Using an
approach [Phys. Rev. A 78, 052101 (2008)] that is not limited to the symmetric
Hilbert space, we explore potential pitfalls in the design and interpretation
of experiments on spin-squeezing and collective atomic phenomena when the
properties of the symmetric states are extended to systems where they do not
apply.Comment: 13 pages, 7 figure
Managing uncertainty through robust-satisficing monetary policy
We employ information-gap decision theory to derive a robust monetary policy response to Knightian parameter uncertainty. This approach provides a quantitative answer to the question: For a specified policy, how much can our models and data err or vary, without rendering the outcome of that policy unacceptable to a policymaker? For a given acceptable level of performance, the policymaker selects the policy that delivers acceptable performance under the greatest range of uncertainty. We show that such information-gap robustness is a proxy for probability of policy success. Hence, policies that are likely to succeed can be identified without knowing the probability distribution. We adopt this approach to investigate empirically the robust monetary policy response to a supply shock with an uncertain degree of persistence.Knightian uncertainty, Monetary policy, Info-gap decision theory.
Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing
We study the strong coupling between photons and atoms that can be achieved
in an optical nanofiber geometry when the interaction is dispersive. While the
Purcell enhancement factor for spontaneous emission into the guided mode does
not reach the strong-coupling regime for individual atoms, one can obtain high
cooperativity for ensembles of a few thousand atoms due to the tight
confinement of the guided modes and constructive interference over the entire
chain of trapped atoms. We calculate the dyadic Green's function, which
determines the scattering of light by atoms in the presence of the fiber, and
thus the phase shift and polarization rotation induced on the guided light by
the trapped atoms. The Green's function is related to a full
Heisenberg-Langevin treatment of the dispersive response of the quantized field
to tensor polarizable atoms. We apply our formalism to quantum nondemolition
(QND) measurement of the atoms via polarimetry. We study shot-noise-limited
detection of atom number for atoms in a completely mixed spin state and the
squeezing of projection noise for atoms in clock states. Compared with
squeezing of atomic ensembles in free space, we capitalize on unique features
that arise in the nanofiber geometry including anisotropy of both the intensity
and polarization of the guided modes. We use a first principles stochastic
master equation to model the squeezing as function of time in the presence of
decoherence due to optical pumping. We find a peak metrological squeezing of ~5
dB is achievable with current technology for ~2500 atoms trapped 180 nm from
the surface of a nanofiber with radius a=225 nm.Comment: To be appeared on PR
Collisional-model quantum trajectories for entangled qubit environments
We study the dynamics of quantum systems interacting with a stream of
entangled qubits. Under fairly general conditions, we present a detailed
framework describing the conditional dynamical maps for the system, called
quantum trajectories, when the qubits are measured. Depending on the
measurement basis, these quantum trajectories can be jump-type or
diffusive-type, and they can exhibit features not present with quantum optical
and single-qubit trajectories. As an example, we consider the case of two
remote atoms, where jump-type quantum trajectories herald the birth and death
of entanglement.Comment: 25 pages, 6 figure
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