SUMMARYIndistinguishable quantum states interfere, but the mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Quantum interference imaging can outperform classical imaging or even have entirely new features.Here, we introduce and experimentally demonstrate a quantum imaging concept that relies on the indistinguishability of the possible sources of a photon that remains undetected. Our experiment uses pair creation in two separate down-conversion crystals. While the photons passing through the object are never detected, we obtain images exclusively with the sister photons that do not interact with the object. Therefore the object to be imaged can be either opaque or invisible to the detected photons. Moreover, our technique allows the probe wavelength to be chosen in a range for which suitable sources and/or detectors are unavailable. Our experiment is a prototype in quantum information where knowledge can be extracted by and about a photon that is never detected.2

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...