Quantum chaos with complex, non-periodic orbits

We show that special types of orbits, which are nonperiodic and complex “saddle orbits” (SOs), describe accurately the quantal and experimental current oscillations in the resonant tunneling diode in tilted fields. The SOs solve the puzzle of broad regions of experimental oscillations where we find no real or complex periodic orbit (PO) that can explain the data. The SOs succeed in regimes involving several nonisolated POs, where PO formulas fail. We show that their contribution can, unexpectedly, decay very slowly in the classical limit

Periodic orbit theory for Rydberg atoms in external fields

Although hydrogen in external fields is a paradigm for the application of periodic orbits and the Gutzwiller trace formula to a real system, the trace formula has never been applied successfully to other Rydberg atoms. We show that spectral fluctuations of general Rydberg atoms are given with remarkable precision by the addition of diffractive terms. Previously unknown features in atomic spectra are exposed: there are new modulations that are neither periodic orbits nor combinations of periodic orbits; “core shadowing” generally decreases primitive periodic orbit amplitudes but can also lead to increases

Atoms in double-delta-kicked periodic potentials: Chaos with long-range correlations

We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization

Proposal for a chaotic ratchet using cold atoms in optical lattices

We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t* greater than or equal to t(r). We conclude that the cold atom ratchets require Db/(h) over bar similar to 1, where b is a small deviation from period-one pulses

Split-sideband spectroscopy in slowly modulated optomechanics

Optomechanical coupling between the motion of a mechanical oscillator and a cavity represents a new arena for experimental investigation of quantum effects on the mesoscopic and macroscopic scale. The motional sidebands of the output of a cavity offer ultra-sensitive probes of the dynamics. We introduce a scheme whereby these sidebands split asymmetrically and show how they may be used as experimental diagnostics and signatures of quantum noise limited dynamics. We show split-sidebands with controllable asymmetry occur by simultaneously modulating the light-mechanical coupling g and the mechanical frequency, ${\omega }_{{\rm{M}}}$—slowly and out-of-phase. Such modulations are generic but already occur in optically trapped set-ups where the equilibrium point of the oscillator is varied cyclically. We analyse recently observed, but overlooked, experimental split-sideband asymmetries; although not yet in the quantum regime, the data suggests that split sideband structures are easily accessible to future experiments

Adiabatic dynamical-decoupling-based control of nuclear spin registers

The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins around NV centers in diamond. We obtain a closed-form expression from Landau-Zener theory and show that it reliably describes the dynamics. By identifying robust Floquet states, we show that the technique enables polarization, one-shot flips, and state storage for nuclear spins. These results introduce a control paradigm that combines dynamical decoupling with adiabatic evolution

Quantum noise spectra for periodically driven cavity optomechanics

A growing number of experimental set-ups in cavity optomechanics exploit periodically driven fields. However, such set-ups are not amenable to analysis using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a new method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators (ii) Floquet and (iii) iterative analysis. We prove that (i) and (ii) yield equivalent noise spectra, and find that (iii) is an analytical approximation to (i) for weak modulations. We calculate the noise spectra of a doubly-modulated system describing experiments of levitated particles in hybrid electro-optical traps. We show excellent agreement with Langevin stochastic simulations in the thermal regime and predict squeezing in the quantum regime. Finally, we reveal how experimentally inaccessible spectral components of a modulated system can be measured in heterodyne detection through an appropriate choice of modulation frequencies

Controlling mode orientations and frequencies in levitated cavity optomechanics

Cavity optomechanics offers quantum cooling, quantum control and measurement of small mechanical oscillators. However the optical backactions that underpin quantum control can significantly disturb the oscillator modes: mechanical frequencies are shifted by the optical spring effect and light-matter hybridisation in strong coupling regimes; mechanical modes hybridise with each other via the cavity mode. This is even more pertinent in the field of levitated optomechanics, where optical trapping fully determines the mechanical modes and their frequencies. Here, using the coherent-scattering (CS) set-up that allowed quantum ground state cooling of a levitated nanoparticle, we show that -- when trapping away from a node of the cavity standing wave -- the CS field opposes optical spring shifts and mechanical mode hybridisation. At an optimal cancellation point, independent of most experimental parameters, we demonstrate experimentally that it is possible to strongly cavity cool and control the {\em unperturbed} modes. Suppression of the cavity-induced mode hybridisation in the $x-y$ plane is quantified by measuring the $S_{xy}(\omega)$ correlation spectra which are seen to always be anti-correlated except at the cancellation point where they become uncorrelated. The findings have implications for directional force sensing using CS set-ups