Optical Readout of the Quantum Collective Motion of an Array of Atomic Ensembles

Botter, Thierry; Brooks, Daniel W. C.; Schreppler, Sydney; Brahms, Nathan; Stamper-Kurn, Dan

doi:10.1103/physrevlett.110.153001

Cited by 33 publications

(44 citation statements)

References 31 publications

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“…Detection of a photon lost from the cavity represents a combined measurement of many of the collective modes of the condensate, dictated by the functional form ofŶ , and corresponds to the jump operator of Eq. (38). When the stochastic field ψ(x,t) is close to the initial configuration-assuming that α 0 is macroscopically occupied, but the remaining excitation modes have low population-then Ŷ is approximately…”

Section: Decomposition Into Bogoliubov-de Gennes Modesmentioning

confidence: 99%

“…The atoms, in turn, affect the resonance frequency of the cavity, and the motion of the atoms can then couple to the cavity field through the spatial variation of the atom-light coupling. The transfer of momentum between the cavity photons and the atoms also allows the realization of optomechanical systems, using the motion of BECs as a mechanical device coupled to the cavity light field [35,37,38]. In the case of atomic BECs, the optomechanical oscillator formed by the atoms is already in the ground state and does not need to be cooled by the cavity field; hence, the general challenge of cooling micromechanical oscillators in optomechanical applications can be circumvented in atomic systems.…”

Section: Introductionmentioning

confidence: 99%

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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: Decomposition Into Bogoliubov-de Gennes Modesmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Following previous work 29 , we trap around 900 atoms in each of two adjacent wells of a superlattice potential, formed by two standing-wave optical fields that are resonant with TEM 00 modes of a Fabry-Perot optical resonator and far detuned from The centre-of-mass motion of each cloud of atoms is linearly coupled to the pump light, creating a system of two optomechanical oscillators. b, Illustration of the realized system of coupled oscillators.…”

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confidence: 99%

Cavity-mediated coupling of mechanical oscillators limited by quantum back-action

et al. 2015

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A complex quantum system can be constructed by coupling simple elements. For example, trapped-ion 1,2 or superconducting 3 quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively, quantum objects can be made to emit and exchange real photons, providing either unidirectional coupling in cascaded geometries 4-6 , or bidirectional coupling that is particularly strong when both objects are placed within a common electromagnetic resonator 7 . However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised by photon loss 8 . Here, we realize phase-coherent interactions between two addressable, spatially separated, near-groundstate mechanical oscillators within a driven optical cavity. We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics [8][9][10][11][12][13][14] .Cavity optomechanical systems comprised of a single mechanical oscillator interacting with a single electromagnetic cavity mode 15 serve useful quantum-mechanical functions, such as generating squeezed light [16][17][18] , detecting forces with quantum-limited sensitivity 19 or through back-action-evading measurement 20 , and both entangling and amplifying mechanical and optical modes 21 . Systems containing several mechanical elements offer additional capabilities. In the quantum regime, these systems may enable two-mode back-action-evading measurements 9 , creation of nonclassical states 10 , fundamental tests of quantum mechanics 8,11,12 , correlations at the quantum level with applications in highsensitivity measurements 13 , and quantum information science 14 . Realizing these proposed functions requires multiple-element cavity optomechanical systems in which quantum-mechanical optical force fluctuations dominate over thermal and technical ones.An important new feature in these multi-mechanical systems is photon-mediated forces between mechanical elements. Consider a driven cavity containing two mechanical elements with linear optomechanical coupling (Fig. 1a). Each element experiences radiation pressure proportional to the number of intracavity photons. The displacement of one element changes the cavity resonance frequency, causing a change in the intracavity photon number, and thereby modifying the force on the second element. In this manner, an effective optical spring is established between the mechanical elements (Fig. 1b). A quantized picture clarifies the role of cavity photons as the bidirectional force-mediating particle for this interaction: pump light is Stokes scattered off one element, generating a cavity photon that is absorbed through anti-Stokes scattering by the second element, and vice versa 7 (Fig. 1c). This cavity-mediated force has been shown to cause hybridization [22][23...

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“…It also naturally applies to cavity QED studies with ensembles, e.g. to investigations of the quantum dynamics of cold atoms in cavity-generated optical potentials [53], to applications involving the simultaneous interaction with multiple standing wave fields [28,54], or to cold atom cavity optomechanics studies [55].…”

Section: Future Prospectsmentioning

confidence: 99%

Sub-micron positioning of trapped ions with respect to the absolute center of a standing-wave cavity field

et al. 2013

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We demonstrate that it is possible, with sub-micron precision, to locate the absolute center of a Fabry-Pérot resonator oriented along the rf-field-free axis of a linear Paul trap through the application of two simultaneously resonating optical fields. In particular, we apply a probe field, which is near-resonant with an electronic transition of trapped ions, simultaneously with an offresonant strong field acting as a periodic AC Stark-shifting potential. Through the resulting spatially modulated fluorescence signal we can find the cavity center of an 11.7 mm-long symmetric FabryPérot cavity with a precision of ±135 nm, which is smaller than the periodicity of the individual standing wave fields. This can e.g. be used to position the minimum of the axial trap potential with respect to the center of the cavity at any location along the cavity mode.

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Optical Readout of the Quantum Collective Motion of an Array of Atomic Ensembles

Cited by 33 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-mediated coupling of mechanical oscillators limited by quantum back-action

Sub-micron positioning of trapped ions with respect to the absolute center of a standing-wave cavity field

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