Achieving coherent quantum control over massive mechanical resonators is a current research goal. Nano- and micromechanical devices can be coupled to a variety of systems, for example to single electrons by electrostatic or magnetic coupling, and to photons by radiation pressure or optical dipole forces. So far, all such experiments have operated in a regime of weak coupling, in which reversible energy exchange between the mechanical device and its coupled partner is suppressed by fast decoherence of the individual systems to their local environments. Controlled quantum experiments are in principle not possible in such a regime, but instead require strong coupling. So far, this has been demonstrated only between microscopic quantum systems, such as atoms and photons (in the context of cavity quantum electrodynamics) or solid state qubits and photons. Strong coupling is an essential requirement for the preparation of mechanical quantum states, such as squeezed or entangled states, and also for using mechanical resonators in the context of quantum information processing, for example, as quantum transducers. Here we report the observation of optomechanical normal mode splitting, which provides unambiguous evidence for strong coupling of cavity photons to a mechanical resonator. This paves the way towards full quantum optical control of nano- and micromechanical devices.

One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Researches are developing various approaches towards such a theory of quantum gravity, but a major hindrance is the lack of experimental evidence of quantum gravitational effects. Yet, the quantization of space-time itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme to experimentally test this conjecture by probing directly the canonical commutation relation of the center-of-mass mode of a mechanical oscillator with a mass close to the Planck mass. Our protocol utilizes quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for table-top experiments to explore possible quantum gravitational phenomena.It is currently an open question whether our underlying concepts of space-time are fully compatible with those of quantum mechanics. The ongoing search for a quantum theory of gravity is therefore one of the main challenges in modern physics. A major difficulty in the development of such theories is the lack of experimentally accessible phenomena that could shed light on the possible route for quantum gravity. Such phenomena are expected to become relevant near the Planck scale, i.e. at energies on the order of the Planck energy E P = 1.2 × 10 19 GeV or at length scales near the Planck length L P = 1.6 × 10 −35 m, where spacetime itself is assumed to be quantized. However, such a minimal length scale is not a feature of quantum theory. The Heisenberg uncertainty relation, one of the cornerstones of quantum mechanics (1), states that the position x and the momentum p of an object cannot be simultaneously known to arbitrary precision. Specifically, the indeterminacies of a joint measurement of these canon- * Electronic address: igor.pikovski@univie.ac.at † Electronic address: m.kim@imperial.ac.uk ical observables are always bound by ∆x∆p ≥ /2. Yet, the uncertainty principle still allows for an arbitrarily precise measurement of only one of the two observables, say position, on the cost of our knowledge about the other (momentum). In stark contrast, in many proposals for quantum gravity the Planck length constitutes a fundamental bound below which position cannot be defined. It has therefore been suggested that the uncertainty relation should be modified in order to take into account such quantum gravitational effects (2). In fact, the concept of a generalized uncertainty principle is found in many approaches to quantum gravity, for example in string theory (3-5), in the theory of doubly special relativity (6, 7), within the principle of relative locality (8) and in studies of black holes (9-11 rent approaches to test quantum gravitational effects mainly ...

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...

Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science 1,2 . Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime 3,4 . We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environment temperature (5 K versus 30 mK). Despite the large laser-added cooling factor of 4,000 and the cryogenic environment, our cooling performance is not limited by residual absorption effects. These results pave the way for the preparation of 100-µm scale objects in the quantum regime. Possible applications range from quantum-limited optomechanical sensing devices to macroscopic tests of quantum physics 5,6 . Recently, the combination of high-finesse optical cavities with mechanical resonators has opened up new possibilities for preparing and detecting mechanical systems close to-and even in-the quantum regime by using well-established methods of quantum optics. Most prominently, the mechanism of efficient laser cooling has been demonstrated 7-13 and has been shown to be capable, in principle, of reaching the quantum ground state [14][15][16] . A particularly intriguing feature of this approach is that it can be applied to mechanical objects of almost arbitrary size, from the nanoscale in microwave strip-line cavities 13 up to the centimetre scale in gravitational-wave interferometers 11 . In addition, whereas quantum-limited readout is still a challenging development step for non-optical schemes 3,17,18 , optical readout techniques at the quantum limit are readily available 19 . Approaching and eventually entering the quantum regime of mechanical resonators through optomechanical interactions essentially requires the following three conditions to be fulfilled: (1) sideband-resolved operation; that is, the cavity amplitude decay rate κ has to be small with respect to the mechanical frequency ω m ; (2) both ultralow noise and low absorption of the optical cavity field (phase noise at the mechanical frequency can act as a finite-temperature thermal reservoir and absorption can increase the mode temperature and even diminish the cavity performance in the case of superconducting cavities); and (3) sufficiently small coupling of the mechanical resonator to the thermal environment; that is, low environment temperature T and large mechanical quality factor Q (the thermal coupling rate is given by k B T / Q, where k B is the Boltzmann constant and is the reduced Planck constant). So far, no experiment has demonstrated all three requirements simultaneously. Criterion (1) has been achieved 10,13,20 ; however, the performance was limited in one case by laser phase noise 10 and in the other cases by absorption in the cavity 13...

Observing a physical quantity without disturbing it is a key capability for the control of individual quantum systems. Such back-action-evading or quantum-non-demolition measurements were first introduced in the 1970s in the context of gravitational wave detection to measure weak forces on test masses by high precision monitoring of their motion. Now, such techniques have become an indispensable tool in quantum science for preparing, manipulating, and detecting quantum states of light, atoms, and other quantum systems. Here we experimentally perform rapid optical quantumnoise-limited measurements of the position of a mechanical oscillator by using pulses of light with a duration much shorter than a period of mechanical motion. Using this back-action evading interaction we performed both state preparation and full state tomography of the mechanical motional state. We have reconstructed mechanical states with a position uncertainty reduced to 19 pm, limited by the quantum fluctuations of the optical pulse, and we have performed 'cooling-by-measurement' to reduce the mechanical mode temperature from an initial 1100 K to 16 K. Future improvements to this technique may allow for quantum squeezing of mechanical motion, even from room temperature, and reconstruction of non-classical states exhibiting negative regions in their phase-space quasi-probability distribution.Experiments are now beginning to investigate nonclassical motion of massive mechanical devices [1][2][3]. This opens up new perspectives for quantum-physics enhanced applications and for tests of the foundations of physics. A versatile approach to manipulate mechanical states of motion is provided by the interaction with electromagnetic radiation, typically confined to microwave or optical cavities. Such cavity-optomechanics experiments [4][5][6][7][8] have thus far largely concentrated on high sensitivity continuous monitoring of the mechanical position [9][10][11][12][13][14]. Because of the back-action imparted by the probe onto the measured object, the precision of such a measurement is fundamentally constrained by the standard quantum limit (SQL) [15,16], and therefore only allows for classical phase-space reconstruction [9,17,18]. In order to observe quantum mechanical features that are smaller than the mechanical zero-point motion, backaction-evading measurement techniques that can surpass the SQL [19,20] are required. Following the early insights of Braginsky, beating the standard quantum limit 'can be achieved only in one way: design the probe so it "sees" only the measured observable ' [15]. Such backaction evading techniques were first realized for the detection of optical quadratures [21][22][23] and have since been used for, e.g. precision measurement of atomic ensemble spin [24][25][26][27][28] and quantum non-demolition microwave photon counting [29]. In optomechanics, to perform a back-action evading measurement of the mechanical position, a time-dependent measurement scheme is required. One prominent example is the so-called 'two-tone app...

Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.

We demonstrate non-degenerate down-conversion at 810 and 1550 nm for long-distance fiber based quantum communication using polarization entangled photon pairs. Measurements of the two-photon visibility, without dark count subtraction, have shown that the quantum correlations (raw visibility 89%) allow secure quantum cryptography after 100 km of non-zero dispersion shifted fiber using commercially available single photon detectors. In addition, quantum state tomography has revealed little degradation of state negativity, decreasing from 0.99 at the source to 0.93 after 100 km, indicating minimal loss in fidelity during the transmission.

Microscale and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example, in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavours. Their performance is in many cases limited by the deleterious effects of mechanical damping. In this study, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators. We begin by introducing an efficient numerical solver, based on the 'phonon-tunnelling' approach, capable of predicting the design-limited damping of high-quality mechanical resonators. Further, through careful device engineering, we isolate support-induced losses and perform a rigorous experimental test of the strong geometric dependence of this loss mechanism. Our results are in excellent agreement with the theory, demonstrating the predictive power of our approach. In combination with recent progress on complementary dissipation mechanisms, our phonon-tunnelling solver represents a major step towards accurate prediction of the mechanical quality factor.