Session U41: Quantum Simulation in Hybrid Systems (and Nano/Optomechanics IV)

Quantum Dynamics of Photon Condensates

Recent experiments have, for the first time, been able to observe the Bose condensation of a gas of weakly interacting photons. We develop a full out-of-equilibrium quantum mechanical treatment of the dynamics of this system. Our model consists of a series of photon modes coupled to the background dye molecules which we simply treat as two-level systems in which each level is separated into a ladder of rovivibration states. We find that the behavior of the photon field is very much like that of a two-level laser in which there is an asymmetry between the effective pump and decay rates induced by the rovivibrational states of the dye. This motivates us to use techniques based on those for the inversionless two-level laser. We are able to calculate the coherence properties of the photons as well as giving insights into the thermalization processes which equilibrate the populations of the various photon modes.   

Excitations of a driven condensate in a cavity: dynamics of the roton-like mode

Recent experiments have demonstrated the superfluid-supersolid quantum phase transition (PT) of an optically driven Bose-Einstein condensate (BEC), via the observation of a roton-like softening of a mode in the Bogoliubov excitation spectrum [1,2]. This phenomenon is usually studied within two-mode approximation for the BEC which results in Dicke-like effective model. In this system, the long-range interactions between the atoms are mediated by cavity photons and the strength of the interactions is controlled by pump power. In this work, we investigate the effect of including the full spectrum of atomic modes. We find a finite lifetime for the roton-like mode below the threshold that is strongly pump-dependent. The corresponding decay rate and critical exponents for the PT are calculated.\\[4pt] [1] K. Baumann, C. Guerlin, F. Brennecke and T. Esslinger, Nature, 464, 1301 (2010).\\[0pt] [2] R. Mottl, F. Brenneck, K. Baumann, R. Landig, T. Donner and T. Esslinger, Science, 336, 1570 (2012).   

Quantum optomechanics in the strong-driving, strong-coupling regime

There is considerable interest in trying to develop quantum optomechanical systems where the coupling is appreciable at the level of a single photon and single phonon. Theoretically, such strongly-coupled optomechanical systems have been largely studied using a polaron transformation in the regime of very weak optical driving. We present here a theoretical approach based on the Keldysh technique that describes single-photon strong coupling physics in an optomechanical system in the presence of a strong optical drive. We show that strong driving can be used to dramatically enhance the effects of the single-photon nonlinearity, leading to striking modifications to the usual linearized optomechanical theory. We discuss the resulting strong modifications of the optomechanically-induced transparency (OMIT) spectrum, a quantity easily accessible in experiment.   

Quantum many body systems with qubits and phonons in the solid state

We previously proposed a nano-mechanical system where phonons trapped in an acoustic cavity can strongly hybridize with impurity qubit states in silicon (forming a so-called cavity-phoniton). Here, we extend the idea to the quantum many-body limit by investigating the physics of phonon-tunnel-coupled arrays of such components. The silicon qubit cavity phoniton system potentially offers advantages in this regime over purely optomechanical systems where the optomechanical coupling is still quite small. First, single phonons in a crystal can have large effective de Broglie wavelengths (microns). Second, as we have previously shown, qubit-phonon coupling can be quite large, easily allowing the system to enter the strong coupling regime and enabling phonon-blockade. Such arrays can be fabricated in semiconductor heterostructures or in on-chip, optomechanical crystals. We calculate the parameter regime where the Mott-Superfluid quantum phase transition occurs in realizable devices. We also demonstrate the emergence of super-splitting, phonon anti-bunching, and phonon blockade through the non-equilibrium density matrix master equation approach in few cavity systems.   

Quantum Dynamics of Optomechanical Arrays

Optomechanical system are typically composed of a single mechanical and a single optical mode interacting via radiation pressure. In this talk, we will introduce an array of optomechanical cells, and discuss our theoretical results on the nonlinear quantum dynamics of such a setup. In particular, we have discovered a phase transition between incoherent mechanical oscillations and a collective phase-coherent mechanical state. We describe how quantum fluctuations drive this transition at low temperatures. We will also discuss the prospects of observing these non-equilibrium dynamics in an experimental implementation based on currently available setups.   

Signatures of nonlinear optomechanics and engineering of nonclassical mechanical steady states

Motivated by recent improvements in coupling strength between light and mechanical motion, we study the strong coupling regime of cavity optomechanics theoretically. We focus on the regime where the optomechanical coupling rate is still small compared to the mechanical resonance frequency, but where the mechanically induced Kerr nonlinearity is significant. The response of the system to an optical drive is characterized. The average photon number in the cavity as a function of drive detuning can feature several peaks due to multi-photon transitions. Furthermore, we show that by optically driving the system at multiple frequencies, multi-photon transitions can facilitate the engineering of nonclassical steady states of the mechanical oscillator.   

Nonlinear Quantum Relaxation and Generation of Non-classical States in Duffing Oscillators

The dissipative quantum dynamics of an anharmonic oscillator is theoretically investigated in the context of carbon-based nano-mechanical systems. In the short-time limit, it is known that macroscopic superposition states appear for such oscillators\footnote{A.~Voje, J.~M.~Kinaret, and A.~Isacsson, Phys.~Rev.~{\bf B85}, 205415 (2012).}. Linear and non-linear dissipation leads to decoherence of such non-classical states in the long-time limit. However, as a result of two-vibron losses at zero temperature, the quantum oscillator eventually evolves into a non-classical stationary state -- a qubit-like state. The relaxation of the qubit due to thermal excitations and one-vibron losses is numerically and analytically studied. The possibility of verifying the occurrence of the qubit is discussed and signatures of the non-classicality arising in a ring-down setup are presented. Additionally, the generation of entanglement between two coupled oscillators in presence of strong two-vibron losses is discussed.   

Parametric feedback squeezing of an opto-electromechanical device below 3dB

Parametric squeezing can reduce the uncertainty in one quadrature of the position of a mechanical resonator, even below the standard quantum limit, and it can improve measurement sensitivity. Here we demonstrate squeezing of the thermal motion of a 570 kHz opto-electromechanical resonator made out of high-stress SiN by modulating its spring constant at twice the resonance frequency. Parametric and direct actuation are achieved by applying a.c. voltages between strongly coupled electrodes on the resonator and a fixed one. It is well know that using this method the motion of one quadrature cannot be decreased more than 3 dB below the undriven case before instabilities kick in. However, by measuring the phase-space trajectory of the resonator and adjusting the phase of the parametric drive in real-time we achieve a stationary reduction in both quadratures that is far beyond this limit. Finally, due to the strong coupling between the drive electrodes, the nonlinearity of the resonator can be tuned all the way from a stiffening spring to a softening one.   

Non-classical correlations of scattered photons in a one-dimensional waveguide with multiple atoms

We study the scaling of photon-photon correlations mediated by resonant interactions of photons with atoms in a one-dimensional photonic waveguide. Recently a new theoretical approach based on the Bethe-ansatz technique has been developed to study transport in an open quantum impurity. Here we generalize the approach to study multiple atoms. We derive the exact solution of single and two-photon scattering states, and the corresponding photon transmission through the atomic ensemble. We show how various two-photon nonlinear effects, such as spatial attraction and repulsion between photons as well as background fluorescence can be tuned by changing the number of atoms and the coupling between atoms (controlled by the separation). Finally we propose a simple scheme for nonreciprocal optical transmission in the waveguide by placing different atoms. Our fully quantum-mechanical approach provides a better understanding of cascaded optical nonlinearity at the microscopic level.   

Recent theoretical advances on superradiant phase transitions

The Dicke model describing a single-mode boson field coupled to two-level systems is an important paradigm in quantum optics. In particular, the physics of ``superradiant phase transitions'' in the ultrastrong coupling regime is the subject of a vigorous research activity in both cavity and circuit QED. Recently, we explored the rich physics of two interesting generalizations of the Dicke model: (i) A model describing the coupling of a boson mode to two independent chains A and B of two-level systems [1], where chain A is coupled to one quadrature of the boson field and chain B to the orthogonal quadrature. This original model leads to a quantum phase transition with a double symmetry breaking and a fourfold ground state degeneracy. (ii) A generalized Dicke model with three-level systems [2,3] including the diamagnetic term. In contrast to the case of two-level atoms for which no-go theorems exist, in the case of three-level system we prove that the Thomas-Reich-Kuhn sum rule does not always prevent a superradiant phase transition.\\[4pt] [1] P. Nataf, A. Baksic and C. Ciuti, Phys. Rev. A {\bf 86}, 013832 (2012).\\[0pt] [2] C. Ciuti and P. Nataf, Phys. Rev. Lett. {\bf 109}, 179301 (2012).\\[0pt] [3] A. Baksic, P. Nataf, and C. Ciuti, arXiv:1206.3213 (2012).   

Light-induced phase transition in a quantum spin chain: Breakdown of the Haldane phase by circularly polarized laser

We theoretically propose a new category of non-equilibrium phase transitions in quantum spin systems that can be induced by the magnetic component of strong lasers. As an example, we consider a Haldane chain with single ion anisotropy radiated by circularly polarized light. We study the spin dynamics by combining the numerical infinite time-evolving block decimation method and an analytical calculation via the Floquet theory, and demonstrate that the laser can magnetize even an antiferromagnet quantum mechanically. It is also shown that the string order is broken by the magnetization, which indicates that a photo-induced breakdown of the Haldane phase has occurred. This phenomenon can be realized using strong THz lasers.   

Testing Kibble-Zurek mechanism in ion traps

A quench through a critical point of a second order phase transition results in the formation of topological defects in the system. Kibble-Zurek (KZ) theory predicts the scaling of a number of defects as a function of quench rate. This scaling depends on the critical exponents of the phase transition, and hence the study of the defect density reveals something about the nature of phase transition itself. There are a number of proposals to test KZ theory experimentally. In this talk, we discuss the possibility of studying defect formation in ion traps. A linear ion chain confined in a Paul trap undergoes a continuous phase transition to a zigzag chain when the confining potential is lowered. If the chain is in a ring trap then the zigzag chain can be in a helical configuration with a nonzero winding number. Using molecular dynamics simulations we show that the scaling of the average winding number of the resulting helical chain is consistent with KZ theory.   

Space-Time Crystals of Trapped Ions

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these spacetime crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.   

Electromagnetic induced transparency and slow light in strongly correlated atomic gases

We develop the quantum theory for the electromagnetic induced transparency (EIT) and slow light property in ultracold Bose and Fermi gases. It shows a very different property from the classical theory which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed dramatically near the Bose-Einstein condensation temperature, while the presence of the Fermi sea can destroy the EIT effect even at zero temperature. This quantum EIT property is mostly manifested in the counter-propagating excitation schemes in either the low-lying Rydberg transition or in D2 transition with a very weak coupling field.\\ Using linear response theory, we further derive an exact and universal form for the EIT spectrum, which applies even in strongly correlated systems of ultracold atoms. We find that the spectrum is closely related to the single particle Green's function, which is not easily observable in most experimental technique. As an example, we show results of 1D Luttinger liquid, Mott-insulator state, and BCS pairing phase, and compare to the results of standard classical theory. Our theory therefore paves the way to measure strongly correlated physics of ultracold atoms via the state-of-art manipulation of light propagation inside the quantum gases.   

Orbital Angular Momentum as Manifestation of Photonic Zitterbewegung

The phenomenon of photonic orbital angular momentum has received considerable attention since its theoretical prediction by Allen et al in 1992. It has been established theoretically and experimentally that laser beams with a Laguerre Gaussian profile possess angular momentum in addition to their intrinsic spin angular momentum. A parallel development has been the renewed interest in zitterbewegung, first predicted for relativistic electrons by Schrodinger. It is now known that zitterebewegung is a property of all particles, regardless of spin, charge or rest mass, since it is basically a quantum mechanical phenomenon. Recently there has arisen an interest in photonic zitterbewegung. This paper shows that photonic orbital angular momentum is one experimentally observable manifestation of photonic zitterbewegung.