Michael R. Hush

Analysis of the operation of gradient echo memories using a quantum input-output model

The gradient echo memory (GEM) technique is a promising candidate for real devices due to its demonstrated performance, but to date high performance experiments can only be described numerically. In this paper we derive a model for GEM as a cascade of infinite interconnected harmonic oscillators. We take a quantum input–output approach to analyse this system, describing the read and write processes of GEM each as a linear-time-invariant process. We provide an analytical solution to the problem in terms of transfer functions which describe the memory behaviour for arbitrary inputs and operating regimes. This allows us to go beyond previous works and analyse the storage quality in the regimes of high optical depth and memory-bandwidth comparable to input bandwidth, exactly the regime of high-efficiency experiments.

Fast machine-learning online optimization of ultra-cold-atom experiments.

We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ‘learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.

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 nondestructive 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 toward the ground state.

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 de Broglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a proper time 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.

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.

Controlling spontaneous-emission noise in measurement-based feedback cooling of a Bose–Einstein condensate

Off-resonant optical imaging is a popular method for continuous monitoring of a Bose–Einstein condensate. However, the disturbance caused by scattered photons places a serious limitation on the lifetime of such continuously monitored condensates. In this paper, we demonstrate that a new choice of feedback control can overcome the heating effects of the measurement backaction. In particular, we show that the measurement backaction caused by off-resonant optical imaging is a multi-mode quantum-field effect, as the entire heating process is not seen in single-particle or mean-field models of the system. Simulating such continuously monitored systems is possible with the number-phase Wigner particle filter, which currently gives both the highest precision and largest timescale simulations amongst competing methods. It is a hybrid between the leading techniques for simulating non-equilibrium dynamics in condensates and particle filters for simulating high-dimensional non-Gaussian filters in the field of engineering. The new control scheme will enable long-term continuous measurement and feedback on one of the leading platforms for precision measurement and the simulation of quantum fields, allowing for the possibility of single-shot experiments, adaptive measurements and robust state-preparation and manipulation.

Coherently tracking the covariance matrix of an open quantum system

Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant and are designed such that some subset of the observers and plants expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and the covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer and find that there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show that it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement because they provide an estimation of a systems quantum state without explicit use of the measurement postulate in their derivation.

Robustness of system-filter separation for the feedback control of a quantum harmonic oscillator undergoing continuous position measurement

We consider the effects of experimental imperfections on the problem of estimation-based feedback control of a trapped particle undergoing continuous position measurement. These limitations violate the assumption that the estimator (i.e., filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We quantify the parameter regimes for stable cooling and show that the control scheme is robust to detector inefficiency, time delay, technical noise, and miscalibrated parameters. We apply these results to the specific context of a weakly-interacting Bose-Einstein condensate (BEC). Given that this system has previously been shown to be less stable than a feedback-cooled BEC with strong interatomic interactions, this result shows that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback.

Cavity driven by a single photon: Conditional dynamics and nonlinear phase shift

We apply the stochastic master equations (quantum filter) derived by Gough et al. (Proc. 50th IEEE Conference on Decision and Control, 2011) to a system consisting of a cavity driven by a multimode single photon field. In particular, we analyse the conditional dynamics for the problem of cross phase modulation in a doubly resonant cavity. Through the exact integration of the stochastic equations, our results reveal features of the problem unavailable from previous models.

Single photon production by rephased amplified spontaneous emission

The production of single photons using rephased amplified spontaneous emission is examined. This process produces single photons on demand with high efficiency by detecting the spontaneous emission from an atomic ensemble, then applying a population-inverting pulse to rephase the ensemble and produce a photon echo of the spontaneous emission events. The theoretical limits on the efficiency of the production are determined for several variants of the scheme. For an ensemble of uniform optical density, generating the initial spontaneous emission and its echo using transitions of different strengths is shown to produce single photons at 70% efficiency, limited by reabsorption. Tailoring the spatial and spectral density of the atomic ensemble is then shown to prevent reabsorption of the rephased photon, resulting in emission efficiency near unity.