Measurement-based quantum control of mechanical motion

Abstract

Controlling a quantum system based on the observation of its dynamics is inevitably complicated by the backaction of the measurement process. Efficient measurements, however, maximize the amount of information gained per disturbance incurred. Real-time feedback then enables both canceling the measurement's backaction and controlling the evolution of the quantum state. While such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, its application to motional degrees of freedom has remained elusive. Here we show measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the soft-clamped resonator in a fraction of its millisecond coherence time, with an overall measurement efficiency close to unity. We use this position record to feedback-cool a resonator mode to its quantum ground state (residual thermal occupationn = 0.29 ± 0.03), 9 dB below the quantum backaction limit of sideband cooling, and six orders of magnitude below the equilibrium occupation of its thermal environment. This realizes a long-standing goal in the field, and adds position and momentum to the degrees of freedom amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational wave detectors. 1 arXiv:1805.05087v2 [quant-ph] 10 Sep 2018Controlling the state of a quantum system is a delicate task, since observation of the system will inevitably perturb it. 1, 2 Coherent quantum control avoids this issue, by coupling the system to another "controller" quantum system in such a way that the joint system converges to the target state without the need for measurement-at the expense of quantum resources in the controller. Measurement-based quantum control 3-5 is based on a different paradigm. It exerts control by measuring the quantum state, and applying feedback that depends on the measurement outcome, much alike classical control systems. In the quantum regime, however, the effect of the measurement's backaction must be taken into account, and effectively canceled. This requires an overall measurement efficiency η-in essence the amount of information gained per decoherence induced-close to unity, a challenging demand yet met only with the impeccable systems of cavity and circuit QED 6, 7 (e.g. η = 40 % in ref. 7 ).To prepare high-purity motional quantum states, researchers have traditionally relied on sideband cooling, a form of coherent quantum control. An engineered quantum optical bath acts as controller, to which the motional degree of freedom couples through optical forces. The motion thermalizes to this bath, at a temperature determined by the forces' quantum fluctuations. This temperature sets a fundamental limit to sideband cooling. In optomechanics, this limit requires that the cavity linewidth resolves the motional sidebands to enable ground state cooling with coherent light. 8 Systems operating in this regime have b...

Spin detection with a micromechanical trampoline: towards magnetic resonance microscopy harnessing cavity optomechanics

“…Further refinements were determined by fitting data to the model provided by equation (7). r m is the radius of the magnetic grain, D ms is the distance between magnetic grain and spin ensemble, D sw is the distance between spin grain and MW stripline, r s is the radius of spin ensemble (cylinder), h s is the height of spin ensemble (cylinder) B 1 is the MW-frequency magnetic field, τ is the relaxation time of spins, B 0 is the uniform magnetic field, and Fabry-Perot cavities with finesse of a few thousand are routinely integrated with membrane resonators [32,38,66,67], and damping rates upward of 10 kHz have been demonstrated in a cryogenic environment down to 100 mK [38]. Note that resonator designs withx 10 zp fm, and  w p2 10MHz m imply structures of ∼10 μm in size.…”

Optimal control for feedback cooling in cavityless levitated optomechanics

“…The ability to precisely control and cool the motion of mechanical resonators in order to generate quantum states is of great interest for testing fundamental physics, such as investigating the quantum-to-classical transition [1,2]. A wide variety of resonator systems have shown promise for achieving such goals, including membranes [3,4], micro-and nano-resonators [5][6][7][8] and cantilevers [9,10]. Although ground state cooling has been experimentally realized in optomechanical systems [3,4,8], there is an appetite to reach such states in levitated systems.…”

Nonlinear dynamics of weakly dissipative optomechanical systems

“…We then compute N(t), the number of trajectories remaining on the chaotic attractor at time t. The escape time can be found from the approximation ( ) ( )  t -N t N t exp 0 e s c . Clearly, numerical approaches cannot distinguish the genuine chaotic trajectories and the transient trajectories with very large t esc 14 . We have used an empirical criterion: (i) trajectories which display chaotic motion during a time interval larger than = W -T 10 m cutoff 5 1 are labeled 'chaotic'; (ii) trajectories whose dynamics remains chaotic only for shorter times and becomes regular afterwards are labeled 'transiently chaotic'.…”

“…For an extended review we refer the reader to [1]. In the past few years, a range of impressive achievements has been observed, which includes topological transport in optomechanical arrays [4,5], the engineering of nonreciprocal interactions [6][7][8][9][10][11], the generation of single phonon states using optical control [12], the generation of mechanical squeezed states [13], measurement-based quantum control of mechanical motion [14], conversion of quantum information to mechanical motion [15], conversion between light in the microwave and optical range [16], single photon frequency shifters [17], force measurements using cold-atom optomechanics [18], and the use of unconventional mechanical modes, like high frequency bulk modes of crystals [19], multilayer graphene [20], and the modes of superfluid helium [21].…”

“…This discussion is, of course, not rigorous, rather illustrative. From a mathematical point of view, the chaotic attractor ceases to exist at η>η c 14. We distinguish here the average escape time τ esc , which is a property of the chaotic attractor, and the escape time t esc , which is a property of the particular trajectory.…”