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Belenchia, Alessio; Carlesso, Matteo; Bayraktar, Ă–mer; Dequal, Daniele; Derkach, Ivan; Gasbarri, Giulio; Herr, Waldemar; Li, Ying Lia; Rademacher, Markus; Sidhu, Jasminder; Oi, Daniel K. L.; Seidel, Stephan T.; Kaltenbaek, Rainer; Marquardt, Christoph; Ulbricht, Hendrik (2022-03-11).
717:{\displaystyle {\ddot {q}}(t)=-\underbrace {\Gamma _{CM}{\dot {q}}(t)} _{\text{damping}}-\underbrace {\omega _{q}^{2}q(t)} _{\text{restoring force}}+\underbrace {\frac {\sqrt {2\pi S_{ff}}}{M}} _{\text{coupling}}+\underbrace {u_{fb}(t)} _{\text{feedback}}}
137:, the Q-factor of a system is often limited by its suspension, which usually demands filigree structures. Nevertheless, the maximally achievable Q-factor usually correlates with the system's size, requiring large systems for achieving high Q-factors.
140:
Particle levitation in external fields can alleviate this constraint. This is one of the reasons why the field of levitated optomechanics has become attractive for research on the foundations in physics and for high-precision applications.
876:). Since that mechanism provides damping, which cools down the mechanical motion, without the introduction of fluctuations, it is referred to as “cold damping”. The first experiment employing this type of cooling was done in 1977 by
299:
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Such quantum states are interesting starting conditions for preparing non-Gaussian quantum states, quantum enhanced sensing, matter-wave interferometry or the realization of entanglement in many-particle systems.
957: to get a signal with twice the frequency of the particle's oscillation. This way the stiffness of the trap increases when the particle moves out of the trap and decreases when the particle is moving back.
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105:. Through the use of levitation, it is possible to decouple the particle's mechanical motion exceptionally well from the environment. This in turn enables the study of high-mass
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756: is the total damping rate, which has usually two dominant contributions: collisions with atoms or molecules of the background gas and photon
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The idea of feedback cooling is to apply a position and/or velocity dependent force on the particle in a way which produces a
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in the regime of quantum physics or for sensing applications, low damping of the oscillator's motion and thus high
1052:
Rademacher, Markus; Konopik, Michael; Debiossac, Maxime; Grass, David; Lutz, Eric; Kiesel, Nikolai (2022-02-15).
98:
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One way to achieve that is by adding a feedback term, which is proportional to the particle's position (
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is the superior approximation and the quantization of the energy levels becomes apparent. The QHO has a
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Ashkin, A.; Dziedzic, J. M. (1977-02-15). "Feedback stabilization of optically levitated particles".
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Instead of applying a linear feedback signal, one can also combine position and velocity via
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of lowest energy where both position and velocity have a minimal variance, determined by the
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1054:"Nonequilibrium Control of Thermal and Mechanical Changes in a Levitated System"
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The external feedback is usually used to cool and control the particle motion.
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1121:"Quantum sensing with nanoparticles for gravimetry: when bigger is better"
294:{\displaystyle {\vec {F}}_{grad}=-\alpha {\vec {\nabla }}{\vec {E}}^{2}/2}
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which deals with the mechanical motion of mesoscopic particles which are
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holds true until one reaches the regime of quantum mechanics, where the
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760:, which becomes dominant below pressures on the order of 10 mbar.
73:
1304:"Dynamics of optically levitated nanoparticles in high vacuum"
1119:
Rademacher, Markus; Millen, James; Li, Ying Lia (2020-11-26).
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The coupling term allows to model any coupling to an external
18:
16:
Field of physics relating to optics and quantum mechanics)
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and provides the basis for precise sensing applications.
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494:, active external feedback and coupling results in the
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1178:Imboden, Matthias; Mohanty, Pritiraj (2014-01-20).
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may be too technical for most readers to understand
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309:, the force can be approximated to first order by
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490: is the particle's mass. Including passive
950:{\displaystyle u_{fb}\propto q(t){\dot {q}}(t)}
1180:"Dissipation in nanoelectromechanical systems"
869:{\displaystyle u_{fb}(t)\propto {\dot {q}}(t)}
463:{\displaystyle \omega _{q}={\sqrt {k_{q}/M}}}
8:
802:Parametric feedback cooling and cold damping
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62:Learn how and when to remove this message
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44:make it understandable to non-experts
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82:, illuminated by a green laser beam
1000:Coherent scattering cavity cooling
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363:{\displaystyle F_{grad,q}=-k_{q}q}
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301:. When a particle is trapped and
78:A silica nanoparticle trapped in
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961:Cavity-enhanced Sisyphus cooling
787:Heisenberg uncertainty principle
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208:is given by the gradient force
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407:{\displaystyle q\in \{x,y,z\}}
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1196:10.1016/j.physrep.2013.09.003
1125:Advanced Optical Technologies
775:classical harmonic oscillator
749:{\displaystyle \Gamma _{CM}}
779:quantum harmonic oscillator
133:are desirable. In nano and
125:In order to use mechanical
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1212:"Quantum physics in space"
201:{\displaystyle {\vec {E}}}
149:The interaction between a
880:, who received the 2018
1269:Applied Physics Letters
1058:Physical Review Letters
773:The approximation of a
169:{\displaystyle \alpha }
87:Levitated optomechanics
1016:This section is empty.
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882:Nobel Prize in Physics
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111:out-of-equilibrium-
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797:Methods of cooling
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99:electrically
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52:January 2023
49:
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498:of motion:
127:oscillators
1321:Categories
1138:2005.14642
1071:2103.10898
1039:References
758:shot noise
151:dielectric
121:Motivation
1289:0003-6951
1254:236881667
1246:0370-1573
1165:219124060
1157:2192-8584
1106:232290453
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933:˙
912:∝
852:˙
843:∝
765:heat bath
735:Γ
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663:⏟
642:π
620:⏟
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585:−
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540:Γ
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414:, i.e. a
381:∈
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272:→
259:→
256:∇
250:α
247:−
223:→
193:→
164:α
113:and nano-
95:optically
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669:coupling
470:, where
580:damping
492:damping
176:and an
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