Squeezing of Quantum Noise of Motion in a Micromechanical Resonator

Abstract

A pair of conjugate observables, such as the quadrature amplitudes of harmonic motion, have fundamental fluctuations that are bound by the Heisenberg uncertainty relation. However, in a squeezed quantum state, fluctuations of a quantity can be reduced below the standard quantum limit, at the cost of increased fluctuations of the conjugate variable. Here we prepare a nearly macroscopic moving body, realized as a micromechanical resonator, in a squeezed quantum state. We obtain squeezing of one quadrature amplitude 1.1 AE 0.4 dB below the standard quantum limit, thus achieving a long-standing goal of obtaining motional squeezing in a macroscopic object. DOI: 10.1103/PhysRevLett.115.243601 PACS numbers: 42.50.Wk, 03.65.Ta, 42.50.Ct, 81.07.Oj The motion xðtÞ ¼ X 1 ðtÞ cosðω m tÞ þ X 2 ðtÞ sinðω m tÞ of a harmonic oscillator having the natural oscillating frequency ω m can be described by the quadrature amplitudes X 1 and X 2 which have slow fluctuations. The fluctuations, presented in units of the quantum zero-point fluctuation amplitude x zp , satisfy the Heisenberg uncertainty relation ΔX 1 ΔX 2 ≥ 1. One of the two can be prepared (¼ squeezed) below the value 1, at the expense of increased fluctuations in the other quadrature. In optics, squeezing of laser light was observed in early 1980s [1,2], not long after the possibility was realized.It has been a formidable challenge to obtain squeezing in the motional state of a macroscopic object. The possibility of squeezing in the oscillations of massive gravitational antennae was hypothesized a long time ago [3,4], but technological limitations are too severe for experimental realization. Other motional quantum-mechanical phenomena, on the other hand, have recently been experimentally demonstrated [5,6] in micromechanical resonators. The latter systems are nearly macroscopic in physical size, and therefore they provide an ideal test system for treating the borderline between quantum and classical. Of particular interest for these studies has been the cavity optomechanics setting coupling electromagnetic cavity mode and the oscillator motion [7]. Output of squeezed light [8][9][10] was recently observed, but this does not yet imply that the oscillator mode is squeezed.Here we report the first realization of squeezing of the motional state of a nearly macroscopic body, realized as a micromechanical resonator measuring 15 microns in diameter. We utilize the novel idea of dissipative squeezing [11][12][13] [see Fig. 1(a)], where the system is allowed to cool towards a squeezed low-energy state. This method has the great advantage of being able to create unconditional squeezing in the steady state. This is in contrast with many other plausible methods of squeezing generation [14][15][16][17][18][19][20]. Our approach is closely related to the quantum nondemolition measurements [21][22][23] which, however, are not able to generate true squeezing without feedback. At this point we mention that classical squeezing of thermal noise is routinely observed in mechanical system...

Non-classical correlations between single photons and phonons from a mechanical oscillator

“…The combination of these techniques allows us to overcome the previous limitations and realize a photon-phonon quantum interface. Our experiment complements previous work on singleand two-mode (opto-)mechanical squeezing in microwave circuits [20][21][22][23]. Although these experiments were based on the same underlying interactions, they involved homodyne or heterodyne detection of light to access continuous-variable degrees of freedom of a quantum state -specifically, quadrature fluctuations in the mechanical and optical canonical variables.…”

“…Further progress in quantum state control has mainly been limited to the domain of electromechanical devices, in which mechanical motion couples to superconducting circuits in the form of qubits and microwave cavities [15]. Recent achievements include single-phonon control of a micromechanical resonator by a superconducting flux qubit [16], the generation of quantum entanglement between quadratures of a microwave cavity field and micromechanical motion [20], and the preparation of quantum squeezed micromechanical states [21][22][23].…”

Entropy production and thermodynamic power of the squeezed thermal reservoir

“…Most commonly considered squeezed states are coherent, but also thermal ones have been largely studied [36,37]. Experimental realizations of squeezed thermal states range from micro-waves [38] to present squeezing of motional degrees of freedom in optomechanical oscillators [39,40].…”

Proposal for an Optomechanical Bell Test

“…DOI: 10.1103/PhysRevLett.116.070405 Introduction.-Cavity optomechanics, which describes a mechanical oscillator controlled by an electromagnetic cavity mode via a generalized radiation pressure force, is the subject of intense research [1][2][3]. Most recent progress includes the cooling of mechanical oscillators down to the ground state [4][5][6], the readout of the mechanical position with a readout imprecision below the standard quantum limit [7] as well as optomechanical squeezing [8,9] and entanglement [10]. Reciprocally, the mechanical degrees of freedom can be used to control the cavity light, e.g., for fast and slow light [11,12], frequency conversions [13,14], squeezing [15], and information storage in long-lived mechanical oscillations [10,16].…”