Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a two-dimensional temporal domain that is treated as a chessboard with one-period x one-period cells. This technique avoids cumulative numerical errors as well as efficiently saves computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically-driven oscillator (degenerate parametric oscillator) below threshold and far away from rotating-wave approximation conditions, which is a relevant scenario for modern low-frequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotating-wave approximation.Comment: Comments and constructive criticism are welcom

On the motion of spinning test particles in plane gravitational waves

The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle in plane gravitational waves are analysed and explicit solutions constructed in terms of solutions of certain linear ordinary differential equations. For harmonic waves this system reduces to a single equation of Mathieu-Hill type. In this case spinning particles may exhibit parametric excitation by gravitational fields. For a spinning test particle scattered by a gravitational wave pulse, the final energy-momentum of the particle may be related to the width, height, polarisation of the wave and spin orientation of the particle.Comment: 11 page

Hyperentanglement-enabled Direct Characterization of Quantum Dynamics

We use hyperentangled photons to experimentally implement an entanglement-assisted quantum process tomography technique known as Direct Characterization of Quantum Dynamics. Specifically, hyperentanglement-assisted Bell-state analysis enabled us to characterize a variety of single-qubit quantum processes using far fewer experimental configurations than are required by Standard Quantum Process Tomography (SQPT). Furthermore, we demonstrate how known errors in Bell-state measurement may be compensated for in the data analysis. Using these techniques, we have obtained single-qubit process fidelities as high as 98.2% but with one-third the number experimental configurations required for SQPT. Extensions of these techniques to multi-qubit quantum processes are discussed.Comment: This is part of a joint submission with an implementation with Ions: "Experimental characterization of quantum dynamics through many-body interactions" by Daniel Nigg, Julio T. Barreiro, Philipp Schindler, Masoud Mohseni, Thomas Monz, Michael Chwalla, Markus Hennrich and Rainer Blat

Transition from quintessence to phantom phase in quintom model

Assuming the Hubble parameter is a continuous and differentiable function of comoving time, we investigate necessary conditions for quintessence to phantom phase transition in quintom model. For power-law and exponential potential examples, we study the behavior of dynamical dark energy fields and Hubble parameter near the transition time, and show that the phantom-divide-line w=-1 is crossed in these models.Comment: LaTeX, 19 pages, four figures, some minor changes in Introduction, two figures added and the references updated, accepted for publication in Phys. Rev.

Direct Characterization of Quantum Dynamics: General Theory

The characterization of the dynamics of quantum systems is a task of both fundamental and practical importance. A general class of methods which have been developed in quantum information theory to accomplish this task is known as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A. Lidar, Phys. Rev. Lett. 97, 170501 (2006)] we presented a new algorithm for Direct Characterization of Quantum Dynamics (DCQD) of two-level quantum systems. Here we provide a generalization by developing a theory for direct and complete characterization of the dynamics of arbitrary quantum systems. In contrast to other QPT schemes, DCQD relies on quantum error-detection techniques and does not require any quantum state tomography. We demonstrate that for the full characterization of the dynamics of n d-level quantum systems (with d a power of a prime), the minimal number of required experimental configurations is reduced quadratically from d^{4n} in separable QPT schemes to d^{2n} in DCQD.Comment: 17 pages, 6 figures, minor modifications are mad

Super-harmonic injection locking of nano-contact spin-torque vortex oscillators

Super-harmonic injection locking of single nano-contact (NC) spin-torque vortex oscillators (STVOs) subject to a small microwave current has been explored. Frequency locking was observed up to the fourth harmonic of the STVO fundamental frequency $f_{0}$ in microwave magneto-electronic measurements. The large frequency tunability of the STVO with respect to $f_{0}$ allowed the device to be locked to multiple sub-harmonics of the microwave frequency $f_{RF}$, or to the same sub-harmonic over a wide range of $f_{RF}$ by tuning the DC current. In general, analysis of the locking range, linewidth, and amplitude showed that the locking efficiency decreased as the harmonic number increased, as expected for harmonic synchronization of a non-linear oscillator. Time-resolved scanning Kerr microscopy (TRSKM) revealed significant differences in the spatial character of the magnetization dynamics of states locked to the fundamental and harmonic frequencies, suggesting significant differences in the core trajectories within the same device. Super-harmonic injection locking of a NC-STVO may open up possibilities for devices such as nanoscale frequency dividers, while differences in the core trajectory may allow mutual synchronisation to be achieved in multi-oscillator networks by tuning the spatial character of the dynamics within shared magnetic layers.Comment: 21 pages, 8 figure

Scattering of Spinning Test Particles by Plane Gravitational and Electromagnetic Waves

The Mathisson-Papapetrou-Dixon (MPD) equations for the motion of electrically neutral massive spinning particles are analysed, in the pole-dipole approximation, in an Einstein-Maxwell plane-wave background spacetime. By exploiting the high symmetry of such spacetimes these equations are reduced to a system of tractable ordinary differential equations. Classes of exact solutions are given, corresponding to particular initial conditions for the directions of the particle spin relative to the direction of the propagating background fields. For Einstein-Maxwell pulses a scattering cross section is defined that reduces in certain limits to those associated with the scattering of scalar and Dirac particles based on classical and quantum field theoretic techniques. The relative simplicity of the MPD approach and its use of macroscopic spin distributions suggests that it may have advantages in those astrophysical situations that involve strong classical gravitational and electromagnetic environments.Comment: Submitted to Classical and Quantum Gravity. 12 page

Quantum Process Estimation via Generic Two-Body Correlations

Performance of quantum process estimation is naturally limited to fundamental, random, and systematic imperfections in preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction due to the fact that standard data analysis techniques presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty state generators and analyzers. Specifically, we present a generalization of "Direct Characterization of Quantum Dynamics" [M. Mohseni and D. A. Lidar, Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that, for several physically relevant noisy preparations and measurements, only classical correlations and small data processing overhead are sufficient to accomplish the full system identification. Furthermore, we provide the optimal input states for which the error amplification due to inversion on the measurement data is minimal.Comment: 7 pages, 2 figure