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arXiv:1803.06767 · Physical Review A

Generation and detection of non-Gaussian phonon-added coherent states in optomechanical systems

Jie Li, Simon Gröblacher, Shi‐Yao Zhu, G. S. Agarwal

Published Jul 2, 2018• 57 citations
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Abstract

Adding excitations on a coherent state provides an effective way to observe the nonclassical properties of radiation fields. Here, we describe and analyze how to apply this concept to the motional state of a mechanical oscillator and present a full scheme to prepare non-Gaussian phonon-added coherent states of the mechanical motion in cavity optomechanics. We first generate a mechanical coherent state using electromagnetically induced transparency. We then add a single phonon onto the coherent state via optomechanical parametric down-conversion combined with single-photon detection. We validate this single-phonon-added coherent state by using a red-detuned beam and reading out the state of the optical output field. This approach allows us to verify nonclassical properties of the phonon state, such as sub-Poissonian character and quadrature squeezing. We further show that our scheme can be directly implemented using existing devices, and is generic in nature and hence applicable to a variety of systems in opto- and electromechanics.

DOI
10.1103/physreva.98.011801

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We show how to use the radiation pressure optomechanical coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state). Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband produces correlated photon-phonon pairs via optomechanical parametric down-conversion. Subsequent detection of a single scattered Stokes photon projects the macroscopic oscillator into a single-phonon Fock state. The nonclassical nature of this mechanical state can be demonstrated by applying a readout laser on the lower sideband to map the phononic state to a photonic mode and performing an autocorrelation measurement. Our approach proves the relevance of cavity optomechanics as an enabling quantum technology.
The preparation of pure quantum states with high degrees of macroscopicity is a central goal of ongoing experimental efforts to control quantum systems. We present a state preparation protocol which renders a mechanical oscillator with an arbitrarily large coherent amplitude in a manifestly nonclassical state. The protocol relies on coherent-state preparation followed by a projective measurement of a single Raman scattered photon, making it particularly suitable for cavity optomechanics. The nonclassicality of the state is reflected by sub-Poissonian phonon statistics, which can be accessed by measuring the statistics of subsequently emitted Raman sideband photons. The proposed protocol would facilitate the observation of nonclassicality of a mechanical oscillator that moves macroscopically relative to motion at the single-phonon level.
In this paper we propose a scheme for the generation of a nonclassical non-Gaussian motional state of a mechanical resonator (MR) in the three-mode optomechanical system in which two linearly coupled single-mode cavities interact dispersively with the mechanical oscillator simultaneously. With one cavity driven by a weak laser field and by properly tuning the driving frequency, a desirable phononic Liouvillian superoperator can be obtained by engineering the selective interaction Hamiltonian confined to Fock subspaces. It is shown that the MR can be driven dissipatively into a steady non-Gaussian nonclassical state, which possesses sub-Poisson statistics, although its Wigner function is positive. The present scheme can be useful for obtaining single phonons.
In this paper, we consider the generation of mechanical squeezed states and single-phonon Fock states, respectively, by homodyne detection and photon subtraction in a dissipative or dispersive optomechanical system under the situation that the cavity linewidth ${\ensuremath{\kappa}}_{c}$ is much larger than the mechanical frequency ${\ensuremath{\omega}}_{m}$. We at first show that strong mechanical squeezing beyond the 3-dB limit can be achieved by homodyning the filtered cavity output field in a purely dispersive or purely dissipative optomechanical system for ${\ensuremath{\kappa}}_{c}\ensuremath{\gg}{\ensuremath{\omega}}_{m}$, while the combination of the two kinds of coupling can also effectively enhance the mechanical squeezing. We next show that in these optomechanical systems, mechanical single-phonon states with high fidelity can be generated via photon subtraction on the filtered cavity output field in the regimes of weak optomechanical entanglement and ${\ensuremath{\kappa}}_{c}\ensuremath{\gg}{\ensuremath{\omega}}_{m}$. It is found that the single-phonon Fock state via purely dissipative optomechanical coupling is attainable in the blue-detuned regime, whereas it is present in the red-detuned regime by purely dispersive optomechanical coupling. In addition, the effects of thermal fluctuations on the mechanical squeezing and the negativity of the Wigner function of the mechanical single-phonon states are also studied. It is shown that the Gaussian squeezing is much more robust against decohering thermal fluctuations than the non-Gaussian nonclassicality.
In this paper, we propose a feasible scheme for generating the Schr\"odinger-cat-like states of a macroscopic mechanical resonator in pulsed cavity optomechanics via photon detection. Starting with cooling the mechanical oscillator to its ground state, a red pulse and a blue pulse with different powers are simultaneously employed to dissipatively generate squeezed mechanical states. Subsequently, a second red pulse is utilized to achieve large-amplitude mechanical catlike states with high fidelities, conditioned on the multiphoton detection of cavity output and assisted by squeezing injection into the cavity. This combination effectively overcomes the difficulty that only a kitten can be produced by single-photon detection. Finally, after being stored in the resonator for a period of time during which thermal effect is analytically revealed, the mechanical quantum superpositions are mapped, with a third red pulse, to the cavity output field for state verification. Our scheme is generic and can also be used to produce other kinds of non-Gaussian mechanical states, such as optical-catalysis nonclassical states.
Coherent interfaces between optical photons and mechanical excitations provide a promising route towards phonon-state engineering and hybrid quantum information processing. Cavity optomechanical systems enable such interfaces via optomechanically induced transparency (OMIT), allowing coherent mapping between traveling optical fields and localized mechanical modes. However, previous implementations of OMIT conversion protocols were limited to classical input signals with large coherent state photon numbers due to room temperature operation and corresponding thermal mechanical noise. Here, we demonstrate efficient low-noise photon-phonon state transfer close to the single-quantum regime in an optomechanical crystal operated at Millikelvin temperatures. Using weak coherent optical input pulses at the few-photon level, we achieve a record-level photon-phonon conversion efficiency of η=0.76η=0.76η=0.76, a mechanical storage lifetime of T1=7.3 μsT_\mathrm{1}=7.3~μsT1​=7.3 μs, and a tunable conversion bandwidth exceeding 4.5 MHz. Hanbury Brown-Twiss measurements of the retrieved signal demonstrate the coherent nature of the converted phononic state, evidencing low added thermal noise in the conversion process (nth=9.0n_\mathrm{th}=9.0nth​=9.0). These results establish optomechanical crystals as efficient optical interfaces to GHz mechanical modes and provide a pathway toward deterministic single-quantum-level mechanical state preparation.