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arXiv:1104.5301 · Physical Review A

Measurement backaction on the quantum spin-mixing dynamics of a spin-1 Bose-Einstein condensate

Keye Zhang, Lu Zhou, Hong Yuan Ling, Han Pu, Weiping Zhang

Published Jun 20, 2011• 8 citations
arXivHTMLPDF

Abstract

We consider a small $F=1$ spinor condensate inside an optical cavity driven by an optical probe field, and subject the output of the probe to a homodyne detection, with the goal of investigating the effect of measurement backaction on the spin dynamics of the condensate. Using the stochastic master equation approach, we show that the effect of backaction is sensitive to not only the measurement strength but also the quantum fluctuation of the spinor condensate. The same method is also used to estimate the atom numbers below which the effect of backaction becomes so prominent that extracting spin dynamics from this cavity-based detection scheme is no longer practical.

DOI
10.1103/physreva.83.063624

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We consider a small F=1F=1F=1 spinor condensate inside an optical cavity driven by an optical probe field, and subject the output of the probe to a homodyne detection, with the goal of investigating the effect of measurement backaction on the spin dynamics of the condensate. Using the stochastic master equation approach, we show that the effect of backaction is sensitive to not only the measurement strength but also the quantum fluctuation of the spinor condensate. The same method is also used to estimate the atom numbers below which the effect of backaction becomes so prominent that extracting spin dynamics from this cavity-based detection scheme is no longer practical.
We provide a theoretical treatment of the quantum backaction of Larmor frequency measurements on a spinor Bose-Einstein condensate by an off-resonant light field. Two main results are presented; the first is a ``quantum jump'' operator description that reflects the abrupt change in the spin state of the atoms when a single photon is counted at a photodiode. The second is the derivation of a conditional stochastic master equation relating the evolution of the condensate density matrix to the measurement record. We provide a few examples of the application of this formalism and comment on its application to metrology.
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We report a spin-orbit-coupling-induced backaction cooling in an optomechanical system, composed of a spin-orbit-coupled Bose-Einstein condensate trapped in an optical cavity with one movable end mirror, by suppressing heating effects of quantum noises. The collective density excitations of the spin-orbit-coupling-mediated hyperfine states---serving as atomic oscillators equally coupled to the cavity field---trigger strongly driven atomic backaction. We find that the backaction not only revamps low-temperature dynamics of its own but also provides an opportunity to cool the mechanical mirror to its quantum-mechanical ground state. Further, we demonstrate that the strength of spin-orbit coupling also superintends dynamic structure factor and squeezes nonlinear quantum noises, like thermomechanical and photon shot noise, which enhances optomechanical features of the hybrid cavity beyond previous investigations. Our findings are testable in a realistic setup and enhance the functionality of cavity optomechanics with spin-orbit-coupled hyperfine states in the field of quantum optics and quantum computation.
Understanding system-reservoir dynamics in many-body physics is a new frontier. An external environment can be thought of as a 'measurement reservoir' which extracts information about the quantum system. Weak (i.e. minimally destructive) measurements provide a time-resolved but noisy record of system evolution. In this talk, we propose using weak measurement and feedback to probe and manipulate spinor Bose-Einstein condensates, focusing on the trade-off between usable information obtained from measurement and the effect of measurement on the system (quantum backaction). As a prototype example, we consider the dynamics of a domain wall in a two-component BEC and show that quantum backaction due to measurement causes two primary effects: domain wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We describe a feedback protocol to create and stabilize a domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.
We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitatively describes the measurement backaction of photon-counting on the homodyne output. The obtained results are applied to typical initial states --- coherent, number, thermal, and squeezed states. Monte Carlo simulations of the measurement processes are also presented to demonstrate the dynamics of the combined measurement process.
We study theoretically the dynamics of a hybrid optomechanical system consisting of a macroscopic mechanical membrane magnetically coupled to a spinor Bose-Einstein condensate via a nanomagnet attached at the membrane center. We demonstrate that this coupling permits us to monitor indirectly the center-of-mass position of the membrane via measurements of the spin of the condensed atoms. These measurements normally induce a significant backaction on the membrane motion, which we quantify for the cases of thermal and coherent initial states of the membrane. We discuss the possibility of measuring this quantum backaction via repeated measurements. We also investigate the potential to generate nonclassical states of the membrane, in particular Schr\"odinger-cat states, via such repeated measurements.