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arXiv:1910.11832 · Physical Review Letters

Observation of Quantum Phase Synchronization in Spin-1 Atoms

Arif Warsi Laskar, Pratik Adhikary, Suprodip Mondal, Parag Katiyar, Sai Vinjanampathy, Saikat Ghosh

Published Jul 1, 2020• 97 citations
arXivHTMLPDF

Abstract

With growing interest in quantum technologies, possibilities of synchronizing quantum systems have garnered significant recent attention. In experiments with dilute ensemble of laser cooled spin-1 ^{87}Rb atoms, we observe phase difference of spin coherences to synchronize with phases of external classical fields. An initial limit-cycle state of a spin-1 atom localizes in phase space due to dark-state polaritons generated by classical two-photon tone fields. In particular, when the two couplings fields are out of phase, the limit-cycle state synchronizes only with two artificially engineered, anisotropic decay rates. Furthermore, we observe a blockade of synchronization due to quantum interference and emergence of Arnold-tongue-like features. Such anisotropic decay induced synchronization of spin-1 systems with no classical analog can provide insights in open quantum systems and find applications in synchronized quantum networks.

DOI
10.1103/physrevlett.125.013601

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With growing interest in quantum technologies, possibilities of synchronizing quantum systems have garnered significant recent attention. In experiments with dilute ensemble of laser cooled spin-1 ^{87}Rb atoms, we observe phase difference of spin coherences to synchronize with phases of external classical fields. An initial limit-cycle state of a spin-1 atom localizes in phase space due to dark-state polaritons generated by classical two-photon tone fields. In particular, when the two couplings fields are out of phase, the limit-cycle state synchronizes only with two artificially engineered, anisotropic decay rates. Furthermore, we observe a blockade of synchronization due to quantum interference and emergence of Arnold-tongue-like features. Such anisotropic decay induced synchronization of spin-1 systems with no classical analog can provide insights in open quantum systems and find applications in synchronized quantum networks.
Extending classical synchronization to the quantum domain is of great interest both from the fundamental physics point of view and with a view toward quantum technology applications. This work characterizes phase synchronization of an effective spin-1 system, which is realized by coupling three quantum states with infinite lifetime to auxiliary excited states that have a finite lifetime. Integrating out the excited states, the effective spin-1 model features coherent and incoherent effective couplings. Our key findings are: (i) Phase synchronization can be controlled by adjusting the phases of the couplings to the excited states. (ii) Unlike in the paradigmatic spin-1 system studied in the literature, where the dissipative couplings describe decay into the limit cycle state, the effective spin-1 model investigated in this work is governed by a competition between dissipative decay into and out of the limit cycle state, with the dissipative decay out of the limit cycle state playing a critical role. (iii) We identify a parameter regime where phase synchronization of the effective spin-1 system is -- in the absence of coherent effective couplings -- governed entirely by the effective dissipators. The effective spin-1 model is benchmarked through comparisons with master equation calculations for the full Hilbert space. Physical insights are gained through analytical perturbation theory calculations. Our findings, which are expected to hold for a broad class of energy level and coupling schemes, are demonstrated using hyperfine states of 87^{87}87Rb.
Synchronization, a ubiquitous phenomenon in classical systems, has recently been extended to the quantum domain. Here, we show quantum synchronization of a bosonic mode exhibiting a Fock state-like limit cycle, manifesting as a steady state with a negative Wigner function. We demonstrate that this non-classical state can be phase-locked to an external drive, achieving synchronization within an Arnold tongue regime. We argue that synchronization is a dynamical property and fundamentally tied to the suppression of phase slips, which we show to occur with exponentially decreasing probability. We introduce a novel method to extract the phase slip rate from the Lindblad time evolution of the system. This work opens new avenues for understanding and manipulating non-classical synchronization dynamics.
Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.
We consider a cavity quantum electrodynamics (CQED) setup where an ensemble of spin-1 atoms driven by a classical field interacts with two driven cavity field modes. We show that the two sub-systems - the atoms and the two-mode cavity field, exhibit limit-cycle or quantum synchronization depending on the cavity drive strengths and other system parameters. In order to visualize the limit cycle and synchronization in the field, we introduce generalized two-mode field Husimi-Q function using SU(2) coherent states. For atomic spin states, we make use of spin-1 Husimi-Q function to visualize the same. We further corroborate the occurrence of field synchronization and limit cycle by analyzing U(1)U(1)U(1) symmetry breaking, Wigner quasi-probability distribution, coherence properties of reduced field density matrix. Our results reveal intriguing interplay between the limit-cycle and quantum synchronization behavior, highlighting emergent quantum phenomena in driven dissipative interacting quantum systems. Additionally, we calculate Wehrl mutual information between the two modes and find that the field synchronization and Wehrl mutual information are mutually exclusive. Our study would be important to extract quantum advantages in quantum metrology using coupled atom-cavity systems.
Quantum synchronization has been a subject of intensive research in the last decade. In this Letter, we propose a quantum Liénard system whose classical equivalent features two limit cycles to one of which the system will converge. In the quantum case, both limit cycles coexist in a single steady state. Each of these limit cycles localizes to a distinct phase if coupled to an external drive: one quantum state can thus be assigned two phases. Furthermore, coupling two such oscillators leads to the simultaneous appearance of synchronization and a synchronization blockade. To shed light on this apparent paradoxical result, we introduce finer measures of quantum synchronization.