615 research outputs found
Continuous measurement feedback control of a Bose-Einstein condensate using phase contrast imaging
We consider the theory of feedback control of a Bose-Einstein condensate
(BEC) confined in a harmonic trap under a continuous measurement constructed
via non-destructive imaging. A filtering theory approach is used to derive a
stochastic master equation (SME) for the system from a general Hamiltonian
based upon system-bath coupling. Numerical solutions for this SME in the limit
of a single atom show that the final steady state energy is dependent upon the
measurement strength, the ratio of photon kinetic energy to atomic kinetic
energy, and the feedback strength. Simulations indicate that for a weak
measurement strength, feedback can be used to overcome heating introduced by
the scattering of light, thereby allowing the atom to be driven towards the
ground state.Comment: 4 figures, 11 page
Number-Phase Wigner Representation for Efficient Stochastic Simulations
Phase-space representations based on coherent states (P, Q, Wigner) have been
successful in the creation of stochastic differential equations (SDEs) for the
efficient stochastic simulation of high dimensional quantum systems. However
many problems using these techniques remain intractable over long integrations
times. We present a number-phase Wigner representation that can be unraveled
into SDEs. We demonstrate convergence to the correct solution for an anharmonic
oscillator with small dampening for significantly longer than other phase space
representations. This process requires an effective sampling of a non-classical
probability distribution. We describe and demonstrate a method of achieving
this sampling using stochastic weights.Comment: 7 pages, 1 figur
Number-Phase Wigner Representation for Scalable Stochastic Simulations of Controlled Quantum Systems
Simulation of conditional master equations is important to describe systems
under continuous measurement and for the design of control strategies in
quantum systems. For large bosonic systems, such as BEC and atom lasers, full
quantum field simulations must rely on scalable stochastic methods whose
convergence time is restricted by the use of representations based on coherent
states. Here we show that typical measurements on atom-optical systems have a
common form that allows for an efficient simulation using the number-phase
Wigner (NPW) phase-space representation. We demonstrate that a stochastic
method based on the NPW can converge over an order of magnitude longer and more
precisely than its coherent equivalent. This opens the possibility of realistic
simulations of controlled multi-mode quantum systems.Comment: 5 pages, 1 figur
Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging
The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.013614 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity
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
Sagnac interferometry with a single atomic clock
The Sagnac effect enables interferometric measurements of rotation with high precision. Using matter waves instead of light promises resolution enhancement by orders of magnitude that scales with particle mass. So far, the paradigm for matter wave Sagnac interferometry relies on DeBroglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a propertime difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth. Inspired by this, we investigate an interferometer comprised of a single atomic clock. The Sagnac effect manifests as a phase shift between trapped atoms in different internal states after transportation along closed paths in opposite directions, without any free propagation. With analytic models, we quantify limitations of the scheme arising from atomic dynamics and finite temperature. Furthermore, we suggest an implementation with previously demonstrated technology
Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier
The transmission of an interacting Bose-Einstein condensate incident on a
repulsive Gaussian barrier is investigated through numerical simulation. The
dynamics associated with interatomic interactions are studied across a broad
parameter range not previously explored. Effective 1D Gross-Pitaevskii equation
(GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE)
simulations in order to isolate purely coherent matterwave effects. Quantum
tunneling is then defined as the portion of the GPE transmission not described
by the classical BVE. An exponential dependence of transmission on barrier
height is observed in the purely classical simulation, suggesting that
observing such exponential dependence is not a sufficient condition for quantum
tunneling. Furthermore, the transmission is found to be predominately described
by classical effects, although interatomic interactions are shown to modify the
magnitude of the quantum tunneling. Interactions are also seen to affect the
amount of classical transmission, producing transmission in regions where the
non-interacting equivalent has none. This theoretical investigation clarifies
the contribution quantum tunneling makes to overall transmission in
many-particle interacting systems, potentially informing future tunneling
experiments with ultracold atoms.Comment: Close to the published versio
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