Synchronization has recently been explored deep in the quantum regime with elementary few-level quantum oscillators such as qudits and weakly pumped quantum van der Pol oscillators. To engineer more complex quantum synchronizing systems, it is practically relevant to study composite oscillators built from basic quantum units that are commonly available and offer high controllability. Here we consider a minimal model for a composite oscillator consisting of two interacting qubits coupled to separate baths and show that this system exhibits a wide variety of synchronizing behaviors. We study the phase response of the constituent qubits as well as the system as a whole, when one of the qubits is weakly driven. We consider the thermal baths to have positive as well as effective negative temperatures and discover effects that occur only when the temperatures of the baths for the two qubits are of opposite signs. We propose and analyze a circuit quantum electrodynamics implementation of this model, which exploits recent advances in dissipation engineering to realize effective negative temperature baths. Our work demonstrates the potential for assembling complex quantum synchronizing systems from basic building units, which is of pragmatic importance for advancing the field of quantum synchronization.
Synchronization has recently been explored deep in the quantum regime with elementary few-level quantum oscillators such as qudits and weakly pumped quantum van der Pol oscillators. To engineer more complex quantum synchronizing systems, it is practically relevant to study composite oscillators built from basic quantum units that are commonly available and offer high controllability. Here we consider a minimal model for a composite oscillator consisting of two interacting qubits coupled to separate baths and show that this system exhibits a wide variety of synchronizing behaviors. We study the phase response of the constituent qubits as well as the system as a whole, when one of the qubits is weakly driven. We consider the thermal baths to have positive as well as effective negative temperatures and discover effects that occur only when the temperatures of the baths for the two qubits are of opposite signs. We propose and analyze a circuit quantum electrodynamics implementation of this model, which exploits recent advances in dissipation engineering to realize effective negative temperature baths. Our work demonstrates the potential for assembling complex quantum synchronizing systems from basic building units, which is of pragmatic importance for advancing the field of quantum synchronization.
Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.
High-quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators [N. L\"orch et al., Phys. Rev. Lett. 118, 243602 (2017)]. Here, we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, the two oscillators are entangled in the steady state, as witnessed by the positivity of the logarithmic negativity.
We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behavior of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that, due to the anharmonicity of the nonlinear interaction between the oscillators, the system exhibits phonon blockade in the phase-locking regime, which is a pure nonclassical effect and has not been observed in the classical domain. We also demonstrate that, for coupled anharmonic oscillators, the system shows a multiple resonance phase-locking behavior due to nonlinear interaction. We point out that the synchronization blockade arises due to strong anticorrelation between the oscillators, which leads to phonon antibunching in the same parametric regime. In the anharmonic oscillator case we illustrate the simultaneous occurrence of bunching and antibunching effects as a consequence of simultaneous negative and positive correlation between the anharmonic oscillators. We examine the aforementioned characteristic features in the frequency entrainment of the oscillators using a power spectrum where one can observe normal mode splitting and the Mollow triplet in the strong coupling regime. Finally, we propose a possible experimental realization for the considered system in the trapped ion and optomechanical setting.
A practical quantum computer, if built, would consist of a set of coupled two-level quantum systems (qubits). Among the variety of qubits implemented, solid-state qubits are of particular interest because of their potential suitability for integrated devices. A variety of qubits based on Josephson junctions have been implemented; these exploit the coherence of Cooper-pair tunnelling in the superconducting state. Despite apparent progress in the implementation of individual solid-state qubits, there have been no experimental reports of multiple qubit gates--a basic requirement for building a real quantum computer. Here we demonstrate a Josephson circuit consisting of two coupled charge qubits. Using a pulse technique, we coherently mix quantum states and observe quantum oscillations, the spectrum of which reflects interaction between the qubits. Our results demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states.
Synchronizing a few-level quantum system is of fundamental importance to the understanding of synchronization in the deep quantum regime. Whether a two-level system, the smallest quantum system, can be synchronized has been theoretically debated for the past several years. Here, for the first time, we demonstrate that a qubit can indeed be synchronized to an external driving signal by using a trapped-ion system. By engineering fully controllable gain and damping processes, an ion qubit is locked to the driving signal and oscillates in phase. Moreover, upon tuning the parameters of the driving signal, we observe characteristic features of the Arnold tongue as well. Our measurements agree remarkably well with numerical simulations based on recent theory on qubit synchronization. By synchronizing the basic unit of quantum information, our study opens up the possibility of exploring the application of quantum synchronization to quantum information processing in the near future.
Synchronizing a few-level quantum system is of fundamental importance to the understanding of synchronization in the deep quantum regime. We investigate quantum phase synchronization of a two-level system (qubit) driven by a semiclassical laser field, in the presence of a dissipative environment having finite bath correlation. The phase preference of the qubit is demonstrated through the Husimi Q-function, and the existence of a limit cycle is also shown in our system. Synchronization of the qubit is quantified using the shifted phase distribution. The signature of quantum phase synchronization viz. the Arnold tongue is obtained from the maximal value of the shifted phase distribution. Two distinct types of qubit dynamics are considered depending on the reservoir correlation time being very short and a situation when bath correlation time is finite. When the reservoir’s frequency spectrum is broad and the bath correlation time is short, the qubit’s phase preference vanishes in the long-time limit. In contrast, a finite bath correlation time and narrow spectral density result in persistent long-time phase localization. The synchronization regions are governed by system–environment parameters, with qubit phase synchronization being enhanced when the reservoir exhibits a narrow frequency spectrum.