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Time crystalline structures are characterized by regularity that single-particle or many-body systems manifest in the time domain, closely resembling the spatial regularity of ordinary space crystals. Here we show that time and space crystalline structures can be combined together and even six-dimensional time-space lattices can be realized. As an example, we demonstrate that such time-space crystalline structures can reveal the six-dimensional quantum Hall effect quantified by the third Chern number., Comment: 7 pages + extended version of supplemental material

We study the parity-time (PT) symmetry characteristics and the applications to nonlinear optics in an optical trimer system consisting of two indirectly coupled standing-mode micro-cavities and a two-level quantum emitter (QE) placed at the intersection of two cavities. We find this trimer system can exhibit analogical phenomena as those in typical $$\mathscr{PT}$$ 𝒫 𝒯 -symmetric dimer systems composed of a passive cavity directly coupled to an active cavity. This system, whose $$\mathscr{PT}$$ 𝒫 𝒯 symmetry is demonstrated by our analytic results, can be transformed between the $$\mathscr{PT}$$ 𝒫 𝒯 -symmetric phase and the $$\mathscr{PT}$$ 𝒫 𝒯 -broken phase by adjusting relevant system parameters. Then, with this system, we observe both the linear and nonlinear parts of the transmission field become remarkably enhanced and can further reach peak values around the $$\mathscr{PT}$$ 𝒫 𝒯 breaking point. In addition, we show the negative correlation between the gain degree of the linear (nonlinear) transmission part and decay rate of the QE. This trimer proposal is feasible for experiments and may provide a promising platform for $$\mathscr{PT}$$ 𝒫 𝒯 -symmetric optics of low-light levels. Moreover, novel phenomena arising from the QE-cavity-coupling induced nonlinearity gain could be explored to fabricate photonic devices and controllable nonlinear optical media for quantum information process and communication of photons.

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.

We study the correlated evolutions of two Rydberg atoms, interacting via a van der Waals (vdW) potential ${V}_{6}$ and driven by a laser field of detunings ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$. The two atoms may exhibit the in-phase dynamics with identical Rydberg populations or the antiphase dynamics with complementary Rydberg populations, depending on their initial states. For a moderate vdW potential far from the blockade regime, the in-phase or antiphase dynamics can be attained along two intersecting lines in the parameter space of ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ with an exact or approximate figure of merit, respectively. Note, in particular, that the exact in-phase dynamics is trivial because it requires identical detunings while the approximate in-phase, exact antiphase, and approximate antiphase dynamics are nontrivial because they require distinct detunings. The specific requirements on ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ for both in-phase and antiphase dynamics can be understood by considering the balanced transitions from two initially populated states to two initially empty states in the double-atom state basis.

We study the correlated evolutions of two far-spaced Rydberg atomic pairs with different resonant frequencies, interacting via van der Waals (vdW) potentials and driven by a common laser field. They are found to exhibit in-phase (anti-phase) beating dynamics characterized by identical (complementary) intra-pair entanglements under a specific condition in regard of inter-pair vdW potentials and driving field detunings. This occurs when each atomic pair just oscillates between its ground state and symmetric entangled state because its doubly excited state and asymmetric entangled state are forbidden due to rigid dipole blockade and perfect destructive interference, respectively. More importantly, optimal inter-pair overall entanglement can be attained at each beating node corresponding to semi-optimal intra-pair entanglements, and inevitable dissipation processes just result in a slow decay of intra-pair and inter-pair entanglements yet without destroying in-phase and anti-phase beating dynamics.

We study the multistability of fixed points for a dimerized system of Rydberg atoms driven by two laser fields and trapped in a two-dimensional (2D) square lattice. For identical driving fields, the fixed points of this system exhibit stable uniform, unstable uniform, stable nonuniform, or oscillating nonuniform phases in the presence of a bistable region. For different driving fields, however, all (stable, unstable, or oscillating) phases become nonuniform instead, which then results in two islets isolated from the mainland of Rydberg excitation. We also show that a tristable region may stretch out from the (nonuniform) bistable region near the islets, indicating that a richer phase diagram can be attained by tuning the Rabi frequencies and/or detunings of the driving fields. Last but not least, the fixed points can adiabatically evolve from the islets to the mainland but can not inversely evolve from the mainland to the islets.

Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g., with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.

We study the optical response of a double optomechanical cavity system assisted by two Rydberg atoms. The target atom is only coupled with one side cavity by a single cavity mode, and gate one is outside the cavities. It has been realized that a long-range manipulation of optical properties of a hybrid system, by controlling the Rydberg atom decoupled with the optomechanical cavity. Switching on the coupling between atoms and cavity mode, the original spatial inversion symmetry of the double cavity structure has been broken. Combining the controllable optical non-reciprocity with the coherent perfect absorption/transmission/synthesis effect (CPA/CPT/CPS reported by [ X.-B. Yan Opt. Express22, 4886 (2014)], we put forward the theoretical schemes of an all-optical transistor which contains functions such as a controllable diode, rectifier, and amplifier by controlling a single gate photon.

We study in theory the single-photon Rydberg excitation in an ensemble of two-level cold atoms at finite low temperatures. Rydberg population plotted against laser detuning may exhibit a nonlinear bistable behavior arising from the dipole–dipole interactions manifested as a van der Waals (vdW) potential. We find that Doppler broadening can result in a remarkable reduction of the bistable region, which may disappear as the atomic temperature increases to a certain value, of the order of tens to hundreds of μK. This special temperature, depending critically on the vdW potential, can be largely raised by partially eliminating the Doppler effect, when a double-photon excitation scheme is used to replace the single-photon excitation scheme.

We study a double-cavity optomechanical system with two movable mirrors acting as mechanical oscillators coupled via a common girder. The fluctuation parts of mechanical oscillations induced by vacuum noises exhibit a limited quantum synchronization owing to the Heisenberg uncertainty. Exerting periodic modulations on the driving lasers or mechanical oscillators, we find that it is viable to attain a 50% ~ 75% enhancement on this quantum synchronization with appropriate modulation frequencies and amplitudes. A direct comparison shows that the optimal modulations on driving lasers are more favorable than the optimal modulations on mechanical oscillators in that the former could result in a greater enhancement than the latter. Our findings should be instructive for further studies on multi-cavity optomechanical systems to pursue a promising platform for quantum information processing.