We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator's mean phonon number n is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 +- 0.22 (corresponding to a mode temperature T = 28 +- 7 microK). We also infer n from the calibrated area of each of the two sidebands, and from the oscillator's total damping. The values of n inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator's temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator.
We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator's mean phonon number n is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 +- 0.22 (corresponding to a mode temperature T = 28 +- 7 microK). We also infer n from the calibrated area of each of the two sidebands, and from the oscillator's total damping. The values of n inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator's temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator.
We consider a system where an optical cavity mode is parametrically coupled to a mechanical oscillator. A laser beam driving the cavity at its resonance frequency will acquire red- and blue-shifted sidebands due to noise in the position of the mechanical oscillator. In a classical theory without noise in the electromagnetic field, the powers of these sidebands are of equal magnitude. In a quantum theory, however, an asymmetry between the sidebands can be resolved when the oscillator's average number of vibrational excitations (phonons) becomes small, i.e., comparable to 1. We discuss the interpretation of this sideband asymmetry in a heterodyne photodetection measurement scheme and show that it depends on the choice of detector model. In the optical regime, standard photodetection theory leads to a photocurrent noise spectrum given by normal- and time-ordered expectation values. The sideband asymmetry is in that case a direct reflection of the quantum asymmetry of the position noise spectrum of the mechanical oscillator. Conversely, for a detector that measures symmetric, nonordered expectation values, we show that the sideband asymmetry can be traced back to quantum optomechanical interference terms. This ambiguity in interpretation applies not only to mechanical oscillators, but to any degree of freedom that couples linearly to noise in the electromagnetic field. Finally, we also compare the quantum theory to a fully classical model, where sideband asymmetry can arise from classical optomechanical interference terms. We show that, due to the oscillator's lack of zero-point motion in a classical theory, the sidebands in the photocurrent spectrum differ qualitatively from those of a quantum theory at sufficiently low temperatures. We discuss the observable consequences of this deviation between classical and quantum theories.
Although they have enabled several advances in the field of optomechanics, optomechanical disk resonators have not yet been operated in the quantum regime. We present the first experimental demonstration of an optomechanical disk resonator prepared in the quantum ground state. With a gigahertz frequency, the mechanical breathing mode of the investigated semiconductor disk reaches a level of excitation below a single phonon when cooled in a dilution refrigerator. We quantify the phonon occupancy of the mechanical mode by performing Brillouin sideband spectroscopy: a conical optical fiber is evanescently coupled to the disk optical whispering-gallery mode, and Stokes and anti-Stokes photons scattered by phonon emission and absorption are counted on a single-photon detector. We measure a suppression of the absorption process corresponding to a phonon occupancy of 0.66±0.20. We experimentally investigate the mechanisms ruling laser-induced heating, which limits the lowest measurable phonon occupancy, and notably witness an extra-cavity heating effect.
A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement (i.e., counting single photons in the sidebands imparted on a laser), we herald the addition and subtraction of single phonons on the 300 K thermal motional state of a 4 GHz mechanical oscillator. To understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator, and we confirm the counterintuitive doubling of the mean phonon number resulting from phonon addition and subtraction.
Summary form only given. We observe the quantized motion of single atoms strongly coupled to a high-finesse optical cavity and investigate dynamics of cavity-assisted atom cooling. Single caesium atoms are trapped in a blue-detuned standing-wave intracavity dipole trap, formed by a lock laser which is used to stabilize the cavity resonance frequency. A probe laser is coupled into the cavity mode and its transmission spectrum is monitored by means of photon-counting heterodyne spectroscopy [2].Measured heterodyne spectra of single atoms in the cavity are shown in Fig. 1 for two different lock-laser intensities and compared with theoretical models. The motional Raman sidebands are offset from the carrier beat signal at 1 MHz by the atomic vibrational frequency (±ν). They show asymmetric lineshapes due to the anharmonicity of the dipole potential.We investigate the dependence of the positions and lineshapes of the motional Raman sidebands on experimantal parameters such as the cavity-atom detuning, and lock-laser intensity. Information on the atomic temperature, cooling and heating rates, as well as the atomic position in the cavity with respect to an antinode of the cavity probe field are found by comparing the observed spectra with theoretical predictions [1]. In addition, this technique can also be used to analyze the cooling dynamics of a cavity-assisted EIT cooling scheme which has been recently studied and demonstrated in [3,4].
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.
In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less