Quantum Control of Qubits and Atomic Motion Using Ultrafast Laser Pulses

Pulsed lasers offer significant advantages over CW lasers in the coherent control of qubits. Here we review the theoretical and experimental aspects of controlling the internal and external states of individual trapped atoms with pulse trains. Two distinct regimes of laser intensity are identified. When the pulses are sufficiently weak that the Rabi frequency $\Omega$ is much smaller than the trap frequency \otrap, sideband transitions can be addressed and atom-atom entanglement can be accomplished in much the same way as with CW lasers. By contrast, if the pulses are very strong (\Omega \gg \otrap), impulsive spin-dependent kicks can be combined to create entangling gates which are much faster than a trap period. These fast entangling gates should work outside of the Lamb-Dicke regime and be insensitive to thermal atomic motion.Comment: 16 pages, 15 figure

Direct absorption imaging of ultracold polar molecules

We demonstrate a scheme for direct absorption imaging of an ultracold ground-state polar molecular gas near quantum degeneracy. A challenge in imaging molecules is the lack of closed optical cycling transitions. Our technique relies on photon shot-noise limited absorption imaging on a strong bound-bound molecular transition. We present a systematic characterization of this imaging technique. Using this technique combined with time-of-flight (TOF) expansion, we demonstrate the capability to determine momentum and spatial distributions for the molecular gas. We anticipate that this imaging technique will be a powerful tool for studying molecular quantum gases.Comment: 4 pages, 4 figure

Non-thermalization in trapped atomic ion spin chains

Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin-models which are heralded by memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.Comment: 14 pages, 5 figures, submitted for edition of Phil. Trans. R. Soc. A on "Breakdown of ergodicity in quantum systems

Controlling the hyperfine state of rovibronic ground-state polar molecules

Ultracold molecules offer entirely new possibilities for the control of quantum processes due to their rich internal structure. Recently, near quantum degenerate gases of molecules have been prepared in their rovibronic ground state. For future experiments, it is crucial to also control their hyperfine state. Here, we report the preparation of a rovibronic ground state molecular quantum gas in a single hyperfine state and in particular in the absolute lowest quantum state. The demonstrated and presented scheme is general for bialkali polar molecules and allows the preparation of molecules in a single hyperfine state or in an arbitrary coherent superposition of hyperfine states. The scheme relies on electric-dipole, two-photon microwave transitions through rotationally excited states and makes use of electric nuclear quadrupole interactions to transfer molecular population between different hyperfine states