Conditional ramsey spectroscopy with synchronized atoms

Collective effects on the performance and stability of quantum heat engines

Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.

Subradiant-to-Subradiant Phase Transition in the Bad Cavity Laser

We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a nonanalytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that the atoms are in a macroscopically entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.

Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators

Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase-reduction theory recently developed for quantum nonlinear oscillators [Y. Kato, N. Yamamoto, and H. Nakao, Phys. Rev. Res. 1, 033012 (2019)10.1103/PhysRevResearch.1.033012], two types of optimization problems, one for the stability and the other for the phase coherence of the entrained state, are considered. The optimal waveforms of the periodic amplitude modulation can be derived by applying the classical optimization methods to the semiclassical phase equation that approximately describes the quantum limit-cycle dynamics. Using a quantum van der Pol oscillator with squeezing and Kerr effects as an example, the performance of optimization is numerically analyzed. It is shown that the optimized waveform for the entrainment stability yields faster entrainment to the driving signal than the case with a simple sinusoidal waveform, while that for the phase coherence yields little improvement from the sinusoidal case. These results are explained from the properties of the phase sensitivity function.

Quantum synchronization of two mechanical oscillators in coupled optomechanical systems with Kerr nonlinearity

We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually through an optical fiber or a phonon tunneling. The cavities are filled with Kerr-type nonlinear medium. It is found that, no matter which the coupling and periodically modulation we choose, both of the quantum synchronization of nonlinear optomechanical system are more appealing than the linear optomechanical system. It is easier to observe greatly enhanced quantum synchronization with Kerr nonlinearity. In addition, the different influences on the quantum synchronization between the two coupling ways and the two modulating ways are compared and discussed.

Synchronization enhancement of indirectly coupled oscillators via periodic modulation in an optomechanical system

We study the synchronization behaviors of two indirectly coupled mechanical oscillators of different frequencies in a doublecavity optomechanical system. It is found that quantum synchronization is roughly vanishing though classical synchronization seems rather good when each cavity mode is driven by an external field in the absence of temporal modulations. By periodically modulating cavity detunings or driving amplitudes, however, it is possible to observe greatly enhanced quantum synchronization accompanied with nearly perfect classical synchronization. The level of quantum synchronization observed here is, in particular, much higher than that for two directly coupled mechanical oscillators. Note also that the modulation on cavity detunings is more appealing than that on driving amplitudes when the robustness of quantum synchronization is examined against the bath’s mean temperature or the oscillators’ frequency difference.

Properties and relative measure for quantifying quantum synchronization

Although quantum synchronization phenomena and corresponding measures have been widely discussed recently, it is still an open question how to characterize directly the influence of nonlocal correlation, which is the key distinction for identifying classical and quantum synchronizations. In this paper, we present basic postulates for quantifying quantum synchronization based on the related theory in Mari's work [Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605], and we give a general formula of a quantum synchronization measure with clear physical interpretations. By introducing Pearson's parameter, we show that the obvious characteristics of our measure are the relativity and monotonicity. As an example, the measure is applied to describe synchronization among quantum optomechanical systems under a Markovian bath. We also show the potential by quantifying generalized synchronization and discrete variable synchronization with this measure.

Quantum Synchronization Blockade: Energy Quantization Hinders Synchronization of Identical Oscillators

Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization, is blocked. We demonstrate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with superconducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.

Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators

We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.

Quantum synchronization in an optomechanical system based on Lyapunov control

We extend the concepts of quantum complete synchronization and phase synchronization, which were proposed in A. Mari et al., Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605, to more widespread quantum generalized synchronization. Generalized synchronization can be considered a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measure are proposed and analyzed in this paper. As examples, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling synchronization system, we purposefully design extra control fields based on Lyapunov control theory. We find that the Lyapunov function can adapt to more flexible control objectives, which is more suitable for generalized synchronization control, and the control fields can be achieved simply with a time-variant voltage. Finally, the existence of quantum entanglement in different generalized synchronizations is also discussed.

Supercooling of Atoms in an Optical Resonator

We investigate laser cooling of an ensemble of atoms in an optical cavity. We demonstrate that when atomic dipoles are synchronized in the regime of steady-state superradiance, the motion of the atoms may be subject to a giant frictional force leading to potentially very low temperatures. The ultimate temperature limits are determined by a modified atomic linewidth, which can be orders of magnitude smaller than the cavity linewidth. The cooling rate is enhanced by the superradiant emission into the cavity mode allowing reasonable cooling rates even for dipolar transitions with ultranarrow linewidth.