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arXiv:2110.00253 · Physical Review Letters

Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency

Mingjie Xin, Wui Seng Leong, Zilong Chen, Yu Wang, Shau-Yu Lan

Published Oct 27, 2021• 33 citations
arXivHTMLPDF

Abstract

Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.

DOI
10.1103/physrevlett.127.183602

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Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.
Quantum squeezed states, with biased quantum noise, have been widely utilized in quantum sensing and quantum error correction applications. However, generating and manipulating these nonclassical states with a large squeezing degree typically requires strong nonlinearity, which inevitably induces additional decoherence that diminishes the overall performance. Here, we demonstrate the generation and amplification of squeezed states in a superconducting microwave cavity with weak Kerr nonlinearity. By subtly engineering an off-resonant microwave drive, we observe cyclic dynamics of the quantum squeezing evolution in a displaced frame of the cavity. Furthermore, we deterministically realize quantum squeezing amplification by alternately displacing the Kerr oscillator using the Trotterization technique, achieving a maximum squeezing degree of 14.6 dB and a squeezing rate of 0.28 MHz. Our demonstrated displacement-enhanced squeezing operation offers a hardware-efficient approach for generating large squeezed states, promising potential applications in quantum-enhanced sensing and quantum information processing.
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.
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.
The frequency of a quantum harmonic oscillator cannot be precisely determined through static measurement strategies on a prepared state. Therefore, dynamical procedures must be employed, involving measurements taken after the system has evolved and encoded the frequency information. This paper explores the precision achievable in a protocol where a known detuning suddenly shifts the oscillator’s frequency, which then reverts to its original value after a specific time interval. Our results demonstrate that the squeezing induced by this frequency jump can effectively enhance the encoding of frequency information, significantly improving the quantum signal-to-noise ratio (QSNR) compared to standard free evolution at the same resource (energy and time) cost. The QSNR exhibits minimal dependence on the actual frequency and increases with both the magnitude of the detuning and the overall duration of the protocol. Furthermore, incorporating multiple frequency jumps into the protocol could further enhance precision, particularly for lower frequency values.
We investigate superpositions of two-mode squeezed states (TMSSs), which have potential applications in quantum information processing and quantum sensing. We study some properties of these nonclassical states such as the statistics of each mode and the degree of entanglement between the two modes, which can be higher than that of a TMSS with the same degree of squeezing. The states we consider can be prepared by inducing two-mode Jaynes-Cummings and anti-Jaynes-Cummings interactions in a system of two modes and a spin-12\frac{1}{2}21​ particle, for instance, in the trapped ion domain, as described here. We show that when two harmonic oscillators are prepared in a superposition of two TMSSs, each reduced single-mode state can be advantageously employed to sense arbitrary displacements of the mode in phase space. The Wigner function of this reduced state exhibits a symmetrical peak centered at the phase-space origin, which has the convenient peculiarity of getting narrower in both quadratures simultaneously as the average photon number increases. This narrow peak can be used as the pointer of our quantum sensor, with its position in phase space indicating the displacement undergone by the oscillator.