Self-organization of a Bose-Einstein condensate in an optical cavity

Nagy, Dávid; Szirmai, G.; Domokos, P.

doi:10.1140/epjd/e2008-00074-6

Cited by 183 publications

(260 citation statements)

References 31 publications

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“…The stochastic noise associated with the intensity measurement of light leaked from the cavity in each individual run of the classical trajectory conditions the We solve the steady-state problem using the classical Gross-Pitaevskii equation approach as detailed in Ref. [42], but calculated for our finite system in the harmonic potential trap. Self-organization is seen to occur for factorsh 0 /h 0 10. dynamical evolution of the atoms inside the cavity and the subsequent measurement record.…”

Section: A Uniformly Driven Systemmentioning

confidence: 99%

Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

Lee

Ruostekoski

2014

Phys. Rev. A

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We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic BoseEinstein condensate contained within an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasiprobability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.

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Section: A Uniformly Driven Systemmentioning

confidence: 99%

Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

Lee

Ruostekoski

2014

Phys. Rev. A

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“…To this end, a quantum degenerate bosonic gas was placed into a high-finesse optical cavity subjected to a transverse off-resonant pump beam. Above a critical pump strength, the feedback between the atomic density distribution and the cavity field leads to a spontaneous formation of a symmetry broken phase in which the atoms form a checkerboard density pattern off which pump light is super-radiantly scattered into the cavity [6,[10][11][12][13][14][15][16]. Details of the steady-state diagram as for example different super-radiant fixed points [17,18], dynamic correlations [19], the damping of quasi-particles [20], self-ordered limit cycles [21], or prethermalization effects [22] have been investigated theoretically.…”

Section: Introductionmentioning

confidence: 99%

Cavity-induced chiral states of fermionic quantum gases

2016

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We investigate ultra-cold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.

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“…In order to overcome this difficulty, in this work the dynamical feedback between atoms and an optical cavity is employed to reach a self-organization of topologically non-trivial phases. One fascinating example for a selforganization of a coupled atom-cavity system has been realized recently by placing a bosonic quantum gas into an optical high-finesse resonator subjected to a perpendicular off-resonant pump beam [10][11][12][13][14]. Above a critical pump strength, the occupation of the cavity mode is stabilized and the bosonic atoms organize into a checkerboard density pattern [12].…”

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confidence: 99%

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

et al. 2016

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We show how a fermionic quantum gas in an optical lattice and coupled to the field of an optical cavity can self-organize into a state in which the spontaneously emerging cavity field amplitude induces an artificial magnetic field. The fermions form either a chiral insulator or a chiral liquid carrying edge currents. The feedback mechanism via the cavity field enables robust and fast switching of the edge currents and the cavity output can be employed for non-destructive measurements of the atomic dynamics. The controlled generation of topologically non-trivial quantum phases is of greatest interest since they possess special properties such as extended edge states that can be well protected against destructive environmental effects[1]. Thus, materials with topological non-trivial properties have the prospect to be utilized for quantum devices and quantum computing. Well known are topological insulators with protected edge currents created in quantum Hall devices [2] by strong magnetic fields.For neutral atoms strong artificial magnetic fields can be created [3] which act similarly as magnetic fields for charged particles. Such artificial magnetic fields have been used in quantum gases confined to optical lattices to realize two showcase models of topologically insulating phases, the Hofstadter model in two-dimensions [4][5][6][7] or on a ladder geometry [8] and the Haldane model [9].Yet, the dynamic control and detection of topologically non-trivial quantum states remains a great challenge. In order to overcome this difficulty, in this work the dynamical feedback between atoms and an optical cavity is employed to reach a self-organization of topologically non-trivial phases. One fascinating example for a selforganization of a coupled atom-cavity system has been realized recently by placing a bosonic quantum gas into an optical high-finesse resonator subjected to a perpendicular off-resonant pump beam [10][11][12][13][14]. Above a critical pump strength, the occupation of the cavity mode is stabilized and the bosonic atoms organize into a checkerboard density pattern [12]. Many different proposals have been put forward to realize the self-organization of more complex quantum phases [13] reaching from the Mott-insulator [15] over fermionic phases [16][17][18][19][20] and disordered structures [21][22][23][24] to phases with spin-orbit coupling [25][26][27].In this work, we engineer a direct coupling mechanism of the cavity photons to the tunneling of atoms in an optical lattice. This is achieved using a Raman transition induced by the combination of a transverse pump beam and the cavity field (Fig. 1). The frequencies of the pump beam and the cavity mode are chosen such that the energy transfer is close to the energy offset between neigh- boring lattice sites. The resulting process represents an effective tunneling of the atoms. Due to the running-wave nature of the pump beam, a phase ϕ can be imprinted onto the tunneling of the atoms around a plaquette in the presence of cavity photons. We demonstrate that due t...

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Self-organization of a Bose-Einstein condensate in an optical cavity

Cited by 183 publications

References 31 publications

Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction

Cavity-induced chiral states of fermionic quantum gases

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

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