Squeezing Enhances Quantum Synchronization.

It is desirable to observe synchronization of quantum systems in the quantum regime, defined by the low number of excitations and a highly nonclassical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelm synchronization in this regime. Here, we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible for small values of squeezing, and in this regime, the states are nonclassical. Furthermore, we show that the quality of synchronization measured by the FWHM of the power spectrum is enhanced with squeezing.

[1]  S. Nigg.  Observing quantum synchronization blockade in circuit quantum electrodynamics , 2017, 1706.04945.

[2]  N. Lörch,et al.  Quantum Synchronization Blockade: Energy Quantization Hinders Synchronization of Identical Oscillators. , 2017, Physical review letters.

[3]  C. Bruder,et al.  Synchronization of an optomechanical system to an external drive , 2017, 1703.04344.

[4]  M. H. Naderi,et al.  Synchronization dynamics of two nanomechanical membranes within a Fabry-Perot cavity , 2017, 1703.01783.

[5]  F. Marquardt,et al.  Quantum-coherent phase oscillations in synchronization , 2016, 1608.03550.

[6]  N. Lörch,et al.  Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators. , 2016, Physical review letters.

[7]  H. Hinrichsen,et al.  Oscillation and synchronization of two quantum self-sustained oscillators , 2015 .

[8]  Florian Marquardt,et al.  Noise-induced transitions in optomechanical synchronization , 2015, 1507.06190.

[9]  Michal Lipson,et al.  Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light. , 2015, Physical review letters.

[10]  V. Giovannetti,et al.  Mutual information as an order parameter for quantum synchronization , 2014, 1412.2585.

[11]  Michael R. Hush,et al.  Spin correlations as a probe of quantum synchronization in trapped ion phonon-lasers , 2014, 1412.1863.

[12]  Christoph Bruder,et al.  Quantum synchronization of two Van der Pol oscillators , 2014, 1406.7134.

[13]  Tony E. Lee,et al.  Entanglement tongue and quantum synchronization of disordered oscillators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  H. Tang,et al.  Photonic cavity synchronization of nanomechanical oscillators. , 2013, Physical review letters.

[15]  Christoph Bruder,et al.  Quantum synchronization of a driven self-sustained oscillator. , 2013, Physical review letters.

[16]  Tony E. Lee,et al.  Quantum synchronization of quantum van der Pol oscillators with trapped ions. , 2013, Physical review letters.

[17]  F. Plastina,et al.  Spontaneous synchronization and quantum correlation dynamics of open spin systems , 2013, 1305.1816.

[18]  M. Roukes,et al.  Phase synchronization of two anharmonic nanomechanical oscillators. , 2013, Physical review letters.

[19]  A Mari,et al.  Measures of quantum synchronization in continuous variable systems. , 2013, Physical review letters.

[20]  Emilio Hernández-García,et al.  Synchronization, quantum correlations and entanglement in oscillator networks , 2013, Scientific Reports.

[21]  Franco Nori,et al.  QuTiP 2: A Python framework for the dynamics of open quantum systems , 2012, Comput. Phys. Commun..

[22]  Tony E. Lee,et al.  Quantum-classical transition of correlations of two coupled cavities , 2012, 1209.0742.

[23]  P. McEuen,et al.  Synchronization of micromechanical oscillators using light , 2011, IEEE Photonic Society 24th Annual Meeting.

[24]  Franco Nori,et al.  QuTiP: An open-source Python framework for the dynamics of open quantum systems , 2011, Comput. Phys. Commun..

[25]  Alejandro Jenkins.  Self-oscillation , 2011, 1109.6640.

[26]  Pere Colet,et al.  Quantum correlations and mutual synchronization , 2011, 1105.4129.

[27]  Florian Marquardt,et al.  Collective dynamics in optomechanical arrays , 2010, 2013 Conference on Lasers & Electro-Optics Europe & International Quantum Electronics Conference CLEO EUROPE/IQEC.

[28]  A. M. Jayich,et al.  Dispersive optomechanics: a membrane inside a cavity , 2008, 0805.3723.

[29]  D L Shepelyansky,et al.  Synchronization and bistability of a qubit coupled to a driven dissipative oscillator. , 2008, Physical review letters.

[30]  M. Imboden,et al.  Synchronized Oscillation in Coupled Nanomechanical Oscillators , 2007, Science.

[31]  Chris Arney.  Sync: The Emerging Science of Spontaneous Order , 2007 .

[32]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[33]  S. Girvin,et al.  Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities. , 2005, Physical review letters.

[34]  King,et al.  Generation of nonclassical motional states of a trapped atom. , 1996, Physical review letters.

[35]  Blatt,et al.  "Dark" squeezed states of the motion of a trapped ion. , 1993, Physical review letters.

[36]  Blatt,et al.  Laser cooling of trapped ions in a standing wave. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[37]  D. Rugar,et al.  Mechanical parametric amplification and thermomechanical noise squeezing. , 1991, Physical review letters.

[38]  Wineland,et al.  Quantum-limited cooling and detection of radio-frequency oscillations by laser-cooled ions. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[39]  S. Strogatz,et al.  Amplitude death in an array of limit-cycle oscillators , 1990 .

[40]  Schleich,et al.  Bifurcation in the phase probability distribution of a highly squeezed state. , 1989, Physical review. A, General physics.

[41]  L. Mandel,et al.  Sub-Poissonian photon statistics in resonance fluorescence. , 1979, Optics letters.

[42]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[43]  Franziska Abend,et al.  Sync The Emerging Science Of Spontaneous Order , 2016 .

[44]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[45]  J. Kurths,et al.  Synchronization: A Universal Concept in Nonlinear Sciences , 2001 .

[46]  Physical Review Letters 63 , 1989 .