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arXiv:2403.18790 · Quantum Science and Technology

Squeezing below the ground state of motion of a continuously monitored levitating nanoparticle

Qiongyuan Wu, Diana A. Chisholm, Rafael Muffato, Tiberius Georgescu, Jack Homans, Hendrik Ulbricht, Matteo Carlesso, Mauro Paternostro

Published Aug 22, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract Squeezing is a crucial resource for quantum information processing and quantum sensing. In levitated nanomechanics, squeezed states of motion can be generated via temporal control of the trapping frequency of a massive particle. However, the amount of achievable squeezing typically suffers from detrimental environmental effects. We propose a scheme for the generation of significant levels of mechanical squeezing in the motional state of a levitated nanoparticle by leveraging on the careful temporal control of the trapping potential. We analyse the performance of such a scheme by fully accounting for the most relevant sources of noise, including measurement backaction. The feasibility of our proposal, which is close to experimental state-of-the-art, makes it a valuable tool for quantum state engineering.

DOI
10.1088/2058-9565/ad7284

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Abstract Squeezing is a crucial resource for quantum information processing and quantum sensing. In levitated nanomechanics, squeezed states of motion can be generated via temporal control of the trapping frequency of a massive particle. However, the amount of achievable squeezing typically suffers from detrimental environmental effects. We propose a scheme for the generation of significant levels of mechanical squeezing in the motional state of a levitated nanoparticle by leveraging on the careful temporal control of the trapping potential. We analyse the performance of such a scheme by fully accounting for the most relevant sources of noise, including measurement backaction. The feasibility of our proposal, which is close to experimental state-of-the-art, makes it a valuable tool for quantum state engineering.
Manipulating the motion of macroscopic objects near their quantum mechanical uncertainties has been desired in diverse fields, including fundamental physics, sensing, and transducers. Despite progress in ground-state cooling of a levitated solid particle, realizing its nonclassical states has been elusive. Here, we demonstrate quantum squeezing of the motion of a single nanoparticle by rapidly varying its oscillation frequency. We reveal appreciable narrowing of the velocity variance to -4.9 ± 0.1 decibels of that of the ground state using free-expansion measurements. Our work shows that a levitated nanoparticle offers an ideal platform for studying nonclassical states of its motion and provides a route to developing applications in quantum sensing and exploring quantum mechanics at a macroscopic scale.
Nonclassical states of nano- and micro-mechanical motion enable measurements beyond the standard quantum limit and constitute a key resource for quantum sensing and metrology. The most strongly squeezed mechanical states to date have been generated with electromechanical platforms under cryogenic refrigeration and using reservoir engineering. To push mechanical systems deeper into the quantum-squeezed regime requires protocols that increase the rate at which squeezing is generated to more strongly overcome the decoherence rate at which state purity is lost. Here, we squeeze the 800 kHz libration mode of a silica nanoparticle optically levitated in vacuum at room temperature. We expose our mechanical oscillator to an optically generated inverted potential, where the squeezing operation proceeds at an exponentially accelerated rate. We reach a squeezed quadrature variance 11 dB below the vacuum fluctuations within 250 ns. Our protocol establishes a new paradigm for generating quantum squeezing of mechanical motion and offers a platform for quantum-enhanced sensing with massive oscillators.
Levitated nanoparticles are a forerunner as an experimental platform to test the limits of quantum mechanics at a macroscopic scale. Some important initial steps have been made towards preparing a macroscopic quantum state of a relatively massive (femtogram) particle. Specifically, the community has achieved ground-state cooling of the center-of-mass motion of a nanoparticle levitated in an optical trap. One crucial further step is now to expand the wavefunction of the particle. This step should happen in the presence of a minimum of decoherence, which makes evolution in an optical trap (inevitably exerting measurement backaction) unsuitable.
Sensing weak forces through observing a mechanical motion near or below its quantum zero-point fluctuation has been desired in diverse areas. While mechanical oscillators have played a crucial role in such studies, their application to free-fall-type sensing has been elusive, in particular in the quantum regime. Here, we demonstrate sensing a static force of the order of 10 zeptonewtons with a levitated nanomechanical oscillator below the zero-point fluctuation through the rapid modulation of its confining potential. We prepare a squeezed state with a reduced velocity uncertainty by abruptly decreasing the potential. Subsequently, we detect the exerted static force through time-of-flight measurements, where we release the nanoparticle from the potential and measure the displacement during a free fall. Furthermore, time-of-flight measurements allow us to perform quantum state tomography of the squeezed state, from which we reconstruct its Wigner quasiprobability distribution and evaluate the Fisher information for the position measurement to quantify the achievable force sensitivity of our protocol. Our results demonstrate that modulating the trap stiffness serves as a crucial technique for quantum-limited force sensing and paves the way to utilize a levitated nanoparticle as a promising sensing platform beyond the quantum limit with a capability of quantum state tomography.
We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility of inverting it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticle's center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments.
We theoretically show that laser recoil heating in free-space levitated optomechanics can be arbitrarily suppressed by shining squeezed light onto an optically trapped nanoparticle. The presence of squeezing modifies the quantum electrodynamical light-matter interaction in a way that enables us to control the amount of information that the scattered light carries about a given mechanical degree of freedom. Moreover, we analyze the trade-off between measurement imprecision and back-action noise and show that optical detection beyond the standard quantum limit can be achieved. We predict that, with state-of-the-art squeezed light sources, laser recoil heating can be reduced by at least 60% by squeezing a single Gaussian mode with an appropriate incidence direction, and by 98% by squeezing a properly mode-matched mode. Our results, which are valid both for motional and librational degrees of freedom, will lead to improved feedback cooling schemes as well as boost the coherence time of optically levitated nanoparticles in the quantum regime.