We demonstrate the feedback control of the internal states of atomic ensembles and their protection against collective noise. Weak measurements with negligible back-action and coherent microwave manipulations are used in a feedback controller to protect a superposition state. The efficiency of the feedback is studied for a simple binary noise model and characterized in terms of the trade-off between information retrieval and destructivity from the optical probe. More complex feedback scenarios are implemented which provide a way towards novel atom interferometry schemes using repeated measurements and feedback.
We demonstrate the feedback control of the internal states of atomic ensembles and their protection against collective noise. Weak measurements with negligible back-action and coherent microwave manipulations are used in a feedback controller to protect a superposition state. The efficiency of the feedback is studied for a simple binary noise model and characterized in terms of the trade-off between information retrieval and destructivity from the optical probe. More complex feedback scenarios are implemented which provide a way towards novel atom interferometry schemes using repeated measurements and feedback.
We demonstrate how to use feedback to control the internal states of trapped coherent ensembles of two-level atoms, and to protect a superposition state against the decoherence induced by a collective noise. Our feedback scheme is based on weak optical measurements with negligible backaction followed by coherent microwave manipulations. The efficiency of the feedback system is studied for a simple binary noise model and characterized in terms of the trade-off between information retrieval and destructivity from the optical probe. We also demonstrate the correction of more general types of collective noise. This technique can be used for the operation of atomic interferometers beyond the standard Ramsey scheme, opening the way towards improved atomic sensors.
Atom interferometry based sensors provide today the most precise measurements of time, inertial forces and magnetic fields. In the common approach, a superposition state is interrogated for a given time interval and finally destructively measured. Conversely, we can repeatedly probe non-destructively the same quantum system and demonstrate efficient measurement schemes using feedback. First, we protect a spin polarized atomic ensemble from the decoherence induced by a synthetic noise. After the noise action, the state of the atomic system is read out with negligible projection using a non-destructive probe, and later corrected with a coherent manipulation to restore the initial state. The efficiency of the feedback scheme is studied versus the strength of the measurement and a maximum is found from the trade-off between information gain and probe destructivity. Our feedback controller is then applied to stabilize a classical local oscillator on a collective quantum state, and this is used in an atomic clock configuration to demonstrate experimentally that in some contexts a hybrid phase and frequency lock can surpass conventional atomic clocks which rely only on a frequency lock.
Weak measurements provide new ways to observe and control quantum systems. Here we use weak non-destructive measurements in a feedback scheme to protect an atomic ensemble in a coherent superposition against a simple decoherence model. The feedback efficiency, defined as the ability to recover the coherence of the initial state, is studied versus the number of photons in the probe beam. This allows us to precisely characterize the trade-off between information retrieval and destructivity. The lifetime of the coherent spin state is increased by one order of magnitude when the correction cycle is iterated.
We consider the decoherence of a pseudospin ensemble under collective random rotations and study, both theoretically and experimentally, how a nondestructive measurement combined with real-time feedback correction can protect the state against such a decoherence process. We theoretically characterize the feedback efficiency with different parameters---coherence, entropy, fidelity---and show that a maximum efficiency is reached in the weak measurement regime, when the projection of the state induced by the measurement is negligible. This article presents in detail the experimental results published previously [T. Vanderbruggen et al., Phys. Rev. Lett. 110, 210503 (2013)], where the feedback scheme stabilizes coherent spin states of trapped ultracold atoms and nondestructively probes them with dispersive optical detection. In addition, we study the influence of several parameters, such as atom number and rotation angle, on the performance of the method. We analyze the various decoherence sources limiting the feedback efficiency and propose a way to mitigate their effect. The results demonstrate the potential of the method for the real-time coherent control of atom interferometers.
Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We have explored new ways to achieve this, through rigorous optimization of the spatial geometry, and through control of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. The relevant figure of merit is the metrologically useful spin squeezing determined by the enhancement in the resolution of rotations of the collective spin, relative to the commonly used spin coherent state. With an optimized free-space geometry, and by using a 2-color probe scheme to suppress tensor light shifts, we achieve 3(2) dB of metrologically useful spin squeezing. We can further increase atom-light coupling by implementing internal state control to prepare spin states with larger initial projection noise relative to the spin coherent state. Under the right conditions this increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. With further internal state control the increased atom-atom entanglement can then be mapped to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N ~ 10⁶ atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. By employing precise internal state control, we have prepared and detected projection noise limited "cat" states (which have initial projection noise that is larger by a factor of 2f = 8 for Cs relative to the spin coherent state) and estimate that we can generate up to 6.0(5) dB of metrologically useful spin squeezing, demonstrating the advantage of using the internal atomic structure as a resource for ensemble control.
We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum nondemolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F=0. We use input-output relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor-of-63 reduction in phase-space volume. The method offers a nonthermal route to generation of exotic entangled states in ultracold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases.