Quantum Motional Sideband Asymmetry in the Presence of Kerr-type Nonlinearities

Sideband asymmetry between the Stokes and anti-Stokes scattering is a signature of the mechanical oscillators in the quantum regime. It has been demonstrated in several optomechanical systems, as a self-calibrated thermometry method. We present motional sideband asymmetry. measurements of a nano-optomechanical system sideband-cooled close to the ground state, probing simultaneously with red- and blue-detuned tones. Due to a Kerr-type nonlinear cavity response, the measurement can exhibit an artificially increased motional sideband asymmetry. We develop a theoretical model based on Floquet theory that accurately describes our observations. This has wide-ranging implications for schemes utilizing multiple probing or pumping tones.

Development of a monolithic near-field optomechanical system

Ryan Daniel Schilling

In the same year as Einstein's annus mirabilis, English engineer and physicist John Flemming patented the first rectifying diode, which he called the "Flemming valve". Einstein's work on the photoelectric effect would change our understanding of the nature of light - a pivotal moment in the development of quantum theory. Flemming's diode would transform our world as well, often pointed to as the beginning of modern electronics. These ideas, born in the same moment, have remained entwined. Quantum theory has been fundamental to transistor development, and that, in turn, led to the computer revolution and accompanying development of silicon manufacturing. The theoretical and technological gifts these ideas have accumulated over the past hundred years are now laid to bare in the field of cavity optomechanics. The silicon technology that owes its very existence to quantum theory is now leveraged to test the limitations of theory and perhaps to exploit quantum resources for a new class of sensors. Micro-, and even nano-scale, optical cavities are coupled to commensurately miniaturized mechanical oscillators, where strong radiation pressure mediated interactions between their corresponding modes can be realized. The fluctuating position of a mechanical element is imprinted on the phase of light circulating within the cavity, while the varying amplitude of the light alters its momentum. Quantum fluctuations are imprinted on the mechanical element by light within the cavity, establishing correlations between its phase and amplitude. Utilizing the optomechanical system developed in this thesis work we are able to observe the signature of these induced correlations, even in the presence of thermal noise at room-temperature. Moreover, we demonstrate the principle by which correlations can be used to cancel measurement back-action, producing a quantum-enhanced sensitivity to external forces. The system in question is also demonstrated to achieve an imprecision more than three orders of magnitude below that at the standard quantum, at room-temperature, which is unprecedented. A strong radiation pressure interaction between a micron-scale mechanical element and an optical cavity has been achieved by taking advantage of many of the powerful tools developed in the context of building modern computers. Using transistor technology in this new context we engineer an optomechanical system that exhibits an exceptionally large contribution of back-action relative to thermal noise. In addition to observing this back-action signature at ambient temperatures, the large interaction strength is applied to the task of laser cooling with a measurement-based feedback scheme. In this framework, we demonstrate the ability to reduce the thermal occupation of a cryogenically cooled mechanical mode by an additional three orders of magnitude, to a mean occupancy of just 5.3 phonons.

EPFL2018

Floquet dynamics in the quantum measurement of mechanical motion

Marie Adrienne Ioannou, Tobias Kippenberg, Nicolas Piro Mastracchio, Liu Qiu, Itay Shomroni

The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: From sideband cooling and backaction-evading measurements to ponderomotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiquitous in optomechanical systems. Specifically, employing multiple probe tones, we perform sideband asymmetry measurements, a macroscopic quantum effect, on a silicon optomechanical crystal sideband cooled to 40% ground-state occupation. We show that the Floquet dynamics, resulting from the presence of multiple pump tones, gives rise to an artificially modified motional sideband asymmetry by redistributing thermal and quantum fluctuations among the initially independently scattered thermomechanical sidebands. For pump tones exhibiting large frequency separation, the dynamics is suppressed and accurate quantum noise thermometry demonstrated. We develop a theoretical model based on Floquet theory that accurately describes our observations. The resulting dynamics can be understood as resulting from a synthetic gauge field among the Fourier modes, which is created by the phase lag of the Kerr-type response. This phenomenon has wide-ranging implications for schemes utilizing several pumping tones, as commonly employed in backaction-evading measurements, dissipative optical squeezing, dissipative mechanical squeezing, and quantum noise thermometry. Our observation may equally well be used for optomechanical Floquet engineering, e.g., generation of topological phases of sound by periodic time modulation.

AMER PHYSICAL SOC2019

Quantum Measurement of Mechanical Motion close to the Standard Quantum Limit

Liu Qiu

In quantum mechanics, the Heisenberg uncertainty principle places a fundamental limit in the measurement precision for certain pairs of physical quantities, such as position and momentum, time and energy or amplitude and phase. Due to the Heisenberg uncertainty principle, any attempt to extract certain information from a quantum object would inevitably perturbitinanunpredictableway. This raises one question,"What is the precision limit in such quantum measurements?" The answer, standard quantum limit (SQL), has been obtained by Braginsky to figure out the fundamental quantum limits of displacement measurement in the context of gravitational wave detection. To circumvent the unavoidable quantum back-action from the priori measurement, quantum non-demolition measurement (QND) methods were introduced by Braginsky and Thorne. To surpass the SQL of the displacement measurement in an interferometer, one can measure only one quadrature of the mechanical motion while give up the information about the other canonically conjugated quadrature. Such measurements can be performed by periodic driving the mechanical oscillator, i.e. the back-action evading (BAE) measurement. Cavity optomechanics provides an ideal table-top platform for the testing of the quantum measurement theory. Mechanical oscillator is coupled to electromagnetic field via radiation pressure, which is enhanced by an optical micro-cavity. Over the last decade, laser cooling has enabled the preparation of mechanical oscillator in the ground state in both optical and microwave systems. BAE measurements of mechanical motion have been allowed in the microwave electromechanical systems, which led to the observations of mechanical squeezing and entanglement. However, despite the theoretical proposal almost 40 years ago, the sub-SQL measurements still remain elusive. This thesis reports our efforts approach the sub-SQL with a highly sideband-resolved silicon optomechanical crystal (OMC) in a 3He buffer gas environment at 2K. The OMC couples an optical mode at telecommunication wavelengths and a colocalized mechanical mode at GHz frequencies. The Helium3 buffer gas environment allows sufficient thermalization of the OMC despite the drastically decreased silicon thermal conductivity. We observe Floquet dynamics in motional sideband asymmetry measurement when employing multiple probe tones. The Floquet dynamics arises due to presence of Kerr-type nonlinearities and gives rise to an artificially modified motional sideband asymmetry, resulting from a synthetic gauge field among the Fourier modes. We demonstrate the first optical continuous two-tone backaction-evading measurement of a localized GHz frequency mechanical mode of silicon OMC close to the ground state by showing the transition from conventional sideband asymmetry to backaction-evading measurement. We discover a fundamental two-tone optomechanical instability and demonstrate its implications on the back-action evading measurement. Such instability imposes a fundamental limitation on other two-tone schemes, such as dissipative quantum mechanical squeezing. We demonstrate state-of-art laser sideband cooling of the mechanical motion to a mean thermal occupancy of 0.09 quantum, which is 7.4dB of the oscillator's zero-point energy and corresponds to 92% ground state probability. This also enables us to observe the dissipative mechanical squeezing below the zero-point motion for the first time with laser light.

EPFL2020