Synchronizing quantum harmonic oscillators through two-level systems

Abstract

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of N oscillators and M (< N ) two-level systems.

Criterion of quantum phase synchronization in continuous variable systems by local measurement

“…2 )] with the parameter being the angle of rotation, and then refer to the picture before and after the transformation as the Schrödinger picture and Single leaking mode picture, respectively. By taking = arctan ( 1 / 2 ) , and imposing| 1 − 2 | ≪ ( 1 2 + 2 2 ) 3/2 / | 1 2 |, |( 1 − 2 )sin cos | ≪ , and 1 2 + 2 2 ≪ 1 2 + 2 2 , the Hamiltonian of the system in the Single leaking mode picture becomes [14]:…”

“…The occurrence of synchronization is first discovered by Huygens in two coupled pendulum clocks, and then has been observed in so many different settings, such as the collective lightning of fireflies, the beating of heart cells and chemical reaction [2]. In classical mechanics, the spontaneous synchronization has been widely studied [5][6][7][8], and there exist standard methods to verify whether the motion of two systems is synchronized [2].In quantum level, the spontaneous synchronization has been considered from different aspects: clock synchronization [9][10][11][12], synchronization in oscillator networks [13][14][15][16][17][18][19][20][21], and synchronization between two atomic ensembles [22]. Notably, due to the absence of the phase space trajectories, the extension of the notion of phase synchronization from classical mechanics to its quantum counterpart is not straightforward [23].…”

Machine Learning Applied to Quantum Synchronization‐Assisted Probing

“…The emergence of quantum synchronization has been recently reported in several systems and, in particular, in spin systems . This phenomenon can emerge not only in the well‐known case of systems exhibiting self‐sustained oscillations, but also during transient dynamics . Furthermore, the role played by dissipation and decoherence in synchronization has been explored not only in transient regimes but also in decoherence free subspaces and in the presence of self‐sustained oscillations (in opto‐mechanichal systems).…”

“…[26,[28][29][30][31][32][33][34] This phenomenon can emerge not only in the well-known case of systems exhibiting self-sustained oscillations, [35][36][37] but also during transient dynamics. [26,28,[31][32][33]38,39] Furthermore, the role played by dissipation and decoherence in synchronization has been explored not only in transient regimes but also in decoherence free subspaces [40] and in the presence of self-sustained oscillations (in opto-mechanichal systems [41] ). In the case of two coupled qubits, even with different frequencies, with a significant imbalance between their losses, both synchronization and anti-synchronization can arise depending on the system parameters.…”

Enhancement of quantum synchronization in optomechanical system by modulating the couplings

“…Moreover, the schemes of realizing quantum synchronization are also proposed both expermantally [21][22][23][24][25] and theoretically [26][27][28][29][30][31]. Remarkably, a lot of new researches and achievements have emerged recently [32][33][34].…”