Session M4: Focus Session: Quantum Control and Measurement

Robust and Inhomogeneous Quantum Control of Cold Atom Qudits

Quantum control over complex systems plays an important role in quantum information science. The use of large state space systems (qudits) may prove advantageous for quantum information tasks if good laboratory tools for qudit control can be developed. We have implemented a protocol for arbitrary unitary transformations in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, driving the system with phase modulated rf and microwave magnetic fields and using the tools of optimal control to find appropriate control waveforms. Robustness against imperfections in the applied fields can be built into the control waveforms by averaging the cost function over a suitable ensemble, e. g., a distribution of static and dynamical variations in bias field strength. Suppression of dynamical errors may prove helpful for qudit control in less than ideal environments such as atoms moving around in the light shift potential of a dipole trap. We have also begun to explore inhomogeneous quantum control, with the goal of performing different unitary transformations on qudits that see different light shifts from an optical addressing field. Ultimately this could lead to addressable unitary control similar to that demonstrated for qubits in optical lattices.   

Unitary Transformations in a Large Hilbert Space

Quantum systems with Hilbert space dimension greater than two (qudits) provide an alternative to qubits as carriers of quantum information, and may prove advantageous for quantum information tasks if good laboratory tools for qudit manipulation and readout can be developed. We have implemented a protocol for arbitrary unitary transformations in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, using phase modulated rf and microwave magnetic fields to drive the atomic evolution. Our phase modulation waveforms are designed numerically using a variant of the highly efficient GRAPE algorithm. The fidelity of the resulting transformations is verified experimentally through randomized benchmarking, which indicates an average fidelity better than 97\% across a sample of random unitaries.   

Generating Entangled Spin States for Quantum Metrology by Single-Photon Detection

We present a proposal and latest experimental results on a probabilistic but heralded scheme to generate non-Gaussian entangled states of collective spin in large atomic ensembles by means of single-photon detection. One photon announces the preparation of a Dicke state, while two or more photons announce Schr{\"o}dinger cat states. The entangled states thus produced allow interferometry below the Standard Quantum Limit (SQL). The method produces nearly pure states even for finite photon detection efficiency and weak atom-photon coupling. The entanglement generation can be made quasi-deterministic by means of repeated trial and feedback.   

Atom mediated sensing in a hybrid optomechanical system

A primary difficulty in implementing quantum optomechanical protocols is the requirement to operate in the good cavity limit, i.e., where the cavity linewidth is far smaller than the mechanical frequency. We explore a hybrid two cavity approach in which a membrane-in-the-middle optomechanical cavity is coupled to a second, atomic cavity. Specifically, we show that it is possible to detect the motion of the membrane via an indirect measurement of the atoms. In the case of a non-ideal optomechanical cavity, we show that the sensitivity can be enhanced via this indirect detection. Finally, we investigate the quantum limitations of such a measurement scheme.   

Quantum control for improved metrology

The success of quantum-enhanced sensors relies on precise control of the experimental system to protect them from undesired sources of noise. Unfortunately, simple application of known strategies to reduce decoherence does not necessarily translate into an improvement of phase measurements: the techniques --such as dynamical decoupling -- that eliminate decoherence also eliminate the very signal that one wishes to measure. In this talk I will show how we can extend control techniques to achieve a better and more flexible compromise between sensitivity and noise protection. In addition I will present a novel approach to reconstruct the arbitrary profile of time-varying fields using coherent control of quantum sensors to simultaneously extract information about external fields and correct for unwanted noise sources.   

Quantum-limited measurements of ultracold atoms in an optical cavity

The development of quantum-limited sensors for mechanical signals, such as position, momentum, and force, is a goal common to many active fields of research. Potential applications include strain measurements in large-scale gravitational wave detectors, quantum-limited Casimir force detection, and tests of quantum mechanics on biological structures. I will describe our recent experimental realization of the quantum-limited detection of an externally-applied classical force using an ultracold-atoms-based optomechanical system. The force sensitivity can be tuned across both fundamental measurement regimes, from one limited by probe shot-noise to one dominated by measurement backaction. Our detection technique additionally allows us to construct a phase-space representation of the quantum-limited imprecision of our measurements.   

Quantum Zeno dynamics of a Rydberg atom

The back-action of a quantum measurement can completely modify the evolution of a quantum system. A famous example is the quantum Zeno effect. However, if the eigenspace corresponding to the result of the measurement is degenerated, the evolution of system is no longer freezed, but the dynamics is confined inside the eigenspace. This is the Quantum Zeno Dynamics (QZD). We have experimentally implemented QZD in the Stark manifold of a Rydberg atom. Under the effect of a sigma$+$ radio-frequency field, our atom initially in the circular state behaves as a J$=$25 spin, which rotates between the north pole and the south pole of a generalized Bloch sphere. By repeatedly asking the system ``have you crossed a given latitude?'', we can confine the evolution of the spin to the polar cap of the Bloch sphere. We have recorded the population of the different $m$ sublevels as a function of the RF drive duration to see that the dynamics of the atom is confined in the first states of the spin ladder. We have measured the $Q$ function of the spin for different interaction times, and clearly seen the phase space distribution disappearing from one side of the LL and reappearing on the other, while being transiently in a superposition of two spin coherent states with different phases. To demonstrate the quantum coherence of this superposition, we have reconstructed the full density matrix of the atom at this time.