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arXiv:1211.2870 · Physical Review A

Quantum backaction in spinor-condensate magnetometry

Steven Steinke, Swati Singh, Pierre Meystre, Keith Schwab, Mukund Vengalattore

Published Dec 3, 2013• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.063809

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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.
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 describe a compact, robust and versatile system for studying the macroscopic spin dynamics in a spinor Bose–Einstein condensate. Condensates of are produced by all-optical evaporation in a 1560 nm optical dipole trap, using a non-standard loading sequence that employs an ancillary 1529 nm beam for partial compensation of the strong differential light-shift induced by the dipole trap itself. We use near-resonant Faraday rotation probing to non-destructively track the condensate magnetization, and demonstrate few-Larmor-cycle tracking with no detectable degradation of the spin polarization. In the ferromagnetic F = 1 ground state, we observe the spin orientation between atoms in the condensate is preserved, such that they precess all together like one large spin in the presence of a magnetic field. We characterize this dynamics in terms of the single-shot magnetic coherence times and , and observe them to be of several seconds, limited only by the residence time of the atoms in the trap. At the densities used, this residence is restricted only by one-body losses set by the vacuum conditions.
The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was extended to massive particles more recently. Typically, the interaction between each particle and the detector is assumed to be limited to short time intervals, and the probability of counting particles in one interval is independent of the measurements in previous intervals. There has been some effort to describe particle counting as a continuous measurement, where the detector and the field to be counted interact continuously. However, the formalism based on continuous measurements does not provide a formula applicable to general time- and space-dependent fields. In our work, we derive a fully time- and space-dependent description of the counting process for linear quantum many-body systems, taking into account the back-action of the detector on the field. We apply our formalism to an expanding Bose-Einstein condensate of ultracold atoms, and show that it describes the process correctly, whereas the standard approach gives unphysical results in some limits. The example illustrates that, in certain situations, the back-action of the detector cannot be neglected and has to be included in the description.
Nondestructive imaging of spinor Bose-Einstein condensates (BEC) presents new opportunities for observing and manipulating macroscopic quantum phenomena in real time. In this talk I theoretically study harmonically trapped two-component BECs subject to weak measurement via phase contrast imaging. I discuss the application of weak measurement theory to spatially extended condensates and present a stochastic Gross-Pitaevskii equation for the condensate order parameter. I then examine the stability of spin-polarized and spin-unpolarized phases of the condensate subject to continuous weak measurement. Additionally, I demonstrate how weak measurement can be used to track the position of a domain wall between spin-polarized regions. I quantify the effects of measurement backaction on the stochastic dynamics of the domain wall and discuss how domain wall dynamics could be observed in experiment.
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 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.