7,021 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.
Open Systems Dynamics for Propagating Quantum Fields
In this dissertation, I explore interactions between matter and propagating
light. The electromagnetic field is modeled as a reservoir of quantum harmonic
oscillators successively streaming past a quantum system. Each weak and
fleeting interaction entangles the light and the system, and the light
continues its course. Within the framework of open quantum systems, the light
is eventually traced out, leaving the reduced quantum state of the system as
the primary mathematical subject. Two major results are presented. The first is
a master equation approach for a quantum system interacting with a traveling
wave packet prepared with a definite number of photons. In contrast to
quasi-classical states, such as coherent or thermal fields, these N-photon
states possess temporal mode entanglement, and local interactions in time have
nonlocal consequences. The second is a model for a three-dimensional
light-matter interface for an atomic ensemble interacting with a paraxial laser
beam and its application to the generation of QND spin squeezing. Both coherent
and incoherent dynamics due to spatially inhomogeneous atom-light coupling
across the ensemble are accounted for. Measurement of paraxially scattered
light can generate squeezing of an atomic spin wave, while diffusely scattered
photons lead to spatially local decoherence.Comment: PhD thesis. 261 page
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
Encoding qubits into oscillators with atomic ensembles and squeezed light
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator
provides a number of advantages when used in a fault-tolerant architecture for
quantum computing, most notably that Gaussian operations suffice to implement
all single- and two-qubit Clifford gates. The main drawback of the encoding is
that the logical states themselves are challenging to produce. Here we present
a method for generating optical GKP-encoded qubits by coupling an atomic
ensemble to a squeezed state of light. Particular outcomes of a subsequent spin
measurement of the ensemble herald successful generation of the resource state
in the optical mode. We analyze the method in terms of the resources required
(total spin and amount of squeezing) and the probability of success. We propose
a physical implementation using a Faraday-based quantum non-demolition
interaction.Comment: (v2) consistent with published version; (v1) 16 pages, 5 figure
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