Pulsed quantum optomechanics

Abstract

Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing, and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.optomechanics | quantum measurement | squeezed states C oherent quantum mechanical phenomena, such as entanglement and superposition, are not apparent in the macroscopic realm. It is currently held that on large scales quantum mechanical behavior is masked by decoherence (1) or that quantum mechanical laws may even require modification (2-5). Despite substantial experimental advances, see for example ref. 6, probing this regime remains extremely challenging. Recently however, it has been proposed to utilize the precision and control of quantum optical fields in order to investigate the quantum nature of massive mechanical resonators by means of the radiation-pressure interaction (7-13). Quantum state preparation and the ability to probe the dynamics of mechanical oscillators, the most rigorous method being quantum state tomography, are essential for such investigations. These important elements have been experimentally realized for various quantum systems, e.g., light (14, 15), trapped ions (16, 17), atomic ensemble spin (18,19), and intracavity microwave fields (20). By contrast, an experiment realizing both quantum state preparation and tomography of a mechanical resonator is yet to be achieved. Also, schemes that can probe quantum features without full tomography [e.g., (9, 10, 21)] are similarly challenging. In nanoelectromechanics, cooling of resonator motion and preparation of the ground state have been observed (22, 23) but quantum state reconstruction (24) remains outstanding. In cavity optomechanics significant experimental progress has been made towards quantum state control over mechanical resonators (11-13), which includes classical phase-space monitoring (25,26), laser cooling close to the ground state (27, 28), and low noise continuous measurement of mechanically induced phase fluctuations (29-31). Still, quantum state preparation is technically difficult primarily due to thermal bath coupling and weak radiation-pressure interaction strength, and quantum state reconstruction remains little explored. Thus far, a common theme in proposals for mechanical state reconstruction is state transfer to and then read-out of an auxillary quantum system (32)(33)(34)(35). This technique is a technically demanding approach and remains a c...

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics

“…Using the experimental parameters achieved in this work, a cavity finesse of 10 4 is sufficient. As such a cavity simultaneously requires a high finesse, as well as a large bandwidth to accommodate a short optical pulse, this is best achieved with an optomechanical microcavity [33]. Such improvements to the measurement sensitivity will not only enable Wigner reconstruction with significant negativity but, owing to this pulsed protocol's resilience against mechanical thermal noise, may also allow the generation of non-classical mechanical states in the regime of room temperature quantum optomechanics.…”

“…For an initial thermal state of the mechanical resonator with a large thermal occupation, i.e. χ 2 (1 + 2n) > 1, the means and variances of the mechanical quadratures, upon obtaining the measurement outcome P L are [33]:…”

“…This 'coolingby-measurement' method for entropy reduction, i.e. obtaining mechanical position and then momentum information on the initial state, is rapid and has considerable tolerance to both the initial thermal occupation and the surrounding thermal bath [33]. With future experimental improvements, this scheme allows for the generation of high purity and quantum squeezed states of mechanical motion 'by measurement'.…”

Nonclassical States of Light and Mechanics

“…The optimal transfer is obtained on resonance. A fast, impulsive readout of the mechanical resonator's displacement may be made by injecting a coherent pulse into the cavity and subjecting the output pulse to a homodyne measurement [20]. If we wish to measure the energy of a mechanical resonator we must find an interaction hamiltonian that is at least quadratic in the mechanical amplitude.…”

Optimal quantum parameter estimation in a pulsed quantum optomechanical system

“…Different from the above case of CW laser driving, the so-called pulsed quantum optomechanics [42], is also realized by driving the optical cavity with (very) short optical pulses. Originally, this strategy has been proposed in the systems of qubits [43], and lately extended to atomic ensembles [44] and levitated microspheres trapped in an optical cavity [45].…”