Cavity Cooling of a Levitated Nanosphere by Coherent Scattering

Delić, Uroš; Reisenbauer, Manuel; Grass, David; Kiesel, Nikolai; Vuletić, Vladan; Aspelmeyer, Markus

doi:10.1103/physrevlett.122.123602

Cited by 165 publications

(197 citation statements)

References 52 publications

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“…A comment in this regard is useful: while our calculations assume parameters typical of levitated mechanical systems [33][34][35][36][37][38][39][40][41] and within the grasp or well foreseeable in membrane-based [42] or graphene-based [43] experimental settings, challenges are posed by the arrangement of the geometric configuration specific of our proposal. While the asymmetry of the bidimensional motion addressed in our study does not represent a true difficulty (asymmetric trapping potentials for levitated optomechanical systems are routinely used in current experiments), the small values of the distance between S1 and S2 is the crucial point that requires care.…”

Section: Revelation Strategiesmentioning

confidence: 99%

Testing the gravitational field generated by a quantum superposition

et al. 2019

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What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to witness whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.Quantum field theory is one of the most successful theories ever formulated. All matter fields, together with the electromagnetic and nuclear forces, have been successfully embedded in the quantum framework. They form the standard model of elementary particles, which not only has been confirmed in all advanced accelerator facilities, but has also become an essential ingredient for the description of the Universe and its evolution.In light of this, it is natural to seek a quantum formulation of gravity as well. Yet, the straightforward procedure for promoting the classical field as described by general relativity, into a quantum field, does not work. Several strategies have been put forward, which turned into very sophisticated theories of gravity, the most advanced being string theory and loop quantum gravity. Yet, none of them has reached the goal of providing a fully consistent quantum theory of gravity.At this point, one might wonder whether the very idea of quantizing gravity is correct [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. At the end of the day, according to general relativity, gravity is rather different from all other forces. Actually, it is not a force at all, but a manifestation of the curvature of spacetime, and there is no obvious reason why the standard approach to the quantization of fields should work for spacetime as well. A future unified theory of quantum and gravitational phenomena might require a radical revision not only of our notions of space and time, but also of (quantum) matter. This scenario is growing in likeliness [18][19][20].From the experimental point of view, it has now been ascertained that quantum matter (i.e. matter in a genuine quantum state, such as a coherent superposition state) couples to the Earth's gravity in the most obvious way. This has been confirmed in neutron [21], atom [22] interferometers and used for velocity selection in molecular interferometry [23]. However, in all cases, the gravitational field is classical, i.e. it is generated by a distribution of matter (the Earth) in a fully classical state. Therefore, the pleth...

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Section: Revelation Strategiesmentioning

confidence: 99%

Testing the gravitational field generated by a quantum superposition

et al. 2019

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“…Now, we turn our attention to a system where also the next component is relevant-a levitated particle squeezed by a combination of parametric and dissipative squeezing [36]. The potential for the particle's centre-of-mass motion is defined by the laser beam used for levitation; its scattering into an empty cavity mode provides the optomechanical interaction [46,51,57]. To achieve strong squeezing, the optical tweezer amplitude is modulated at twice the mechanical frequency, E tw (t) = E 0 [1 + α cos(2ω m t)], where α ∈ (0, 1) is the modulation depth, modulating both the mechanical potential and the optomechanical coupling rate.…”

Section: B Parametric and Dissipative Squeezing For A Levitated Partmentioning

confidence: 99%

Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

2020

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Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators. In many applications, linearised form of the interaction is used, which allows for the system dynamics to be fully described using a Lyapunov equation for the covariance matrix of the Wigner function. This approach, however, is problematic in situations where the Hamiltonian becomes time dependent as is the case for systems driven at multiple frequencies simultaneously. This scenario is highly relevant as it leads to dissipative preparation of mechanical states or backaction-evading measurements of mechanical motion. The time-dependent dynamics can be solved with Floquet techniques whose application is, nevertheless, not straightforward. Here, we describe a general method for combining the Lyapunov approach with Floquet techniques that enables us to transform the initial timedependent problem into a time-independent one, albeit in a larger Hilbert space. We show how the lengthy process of applying the Floquet formalism to the original equations of motion and deriving a Lyapunov equation from their time-independent form can be simplified with the use of properly defined Fourier components of the drift matrix of the original time-dependent system. We then use our formalism to comprehensively analyse dissipative generation of mechanical squeezing beyond the rotating wave approximation. Our method is applicable to various problems with multitone driving schemes in cavity optomechanics, electromechanics, and related disciplines. CONTENTS

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“…We now aim to find the threshold of the total laser pump power ζ tot = M ζ for selfordering at the self-consistent temperature T st as a function of χ. Remembering that the stationary state can be approximated by a thermal state in typical parameter regimes [26], we assume that the stationary state is a Boltzmann distribution with the temperature T st and the mean-field potential given in Eq. (8). To obtain the self-consistent cavity fields creating this potential, we employ the method introduced in Ref.…”

Section: Self-ordering Threshold From a Mean-field Modelmentioning

confidence: 99%

Self-ordering and cavity cooling using a train of ultrashort pulses

et al. 2020

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A thin atomic gas in an optical resonator exhibits a phase transition from a homogeneous density to crystalline order when laser illuminated orthogonal to the resonator axis. We study this well-known self-organization phenomenon for a generalized pumping scheme using a femtosecond pulse train with a frequency spectrum spanning a large bandwidth covering many cavity modes. We show that due to simultaneous scattering into adjacent longitudinal cavity modes the induced light forces and the atomic dynamics becomes nearly translation-invariant along the cavity axis. In addition the laser bandwidth introduces a new correlation length scale within which clustering of the atoms is energetically favorable. Numerical simulations allow us to determine the self-consistent ordering threshold power as function of bandwidth and atomic cloud size. We find strong evidence for a change from a second order to a first order self-ordering phase transition with growing laser bandwidth when the size of the atomic cloud gets bigger than the clustering length. An analysis of the cavity output reveals a corresponding transition from a single to a double pulse traveling within the cavity. This doubles the output pulse repetition rate and creates a new time crystal structure in the cavity output. Simulations also show that multi-mode operation significantly improves cavity cooling generating lower kinetic temperatures at a much faster cooling rate.

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Cavity Cooling of a Levitated Nanosphere by Coherent Scattering

Cited by 165 publications

References 52 publications

Testing the gravitational field generated by a quantum superposition

Testing the gravitational field generated by a quantum superposition

Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

Self-ordering and cavity cooling using a train of ultrashort pulses

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