Low-loss transmission and sensitive recovery of weak radio-frequency and microwave signals is a ubiquitous challenge, crucial in radio astronomy, medical imaging, navigation, and classical and quantum communication. Efficient up-conversion of radio-frequency signals to an optical carrier would enable their transmission through optical fibres instead of through copper wires, drastically reducing losses, and would give access to the set of established quantum optical techniques that are routinely used in quantum-limited signal detection. Research in cavity optomechanics has shown that nanomechanical oscillators can couple strongly to either microwave or optical fields. Here we demonstrate a room-temperature optoelectromechanical transducer with both these functionalities, following a recent proposal using a high-quality nanomembrane. A voltage bias of less than 10 V is sufficient to induce strong coupling between the voltage fluctuations in a radio-frequency resonance circuit and the membrane's displacement, which is simultaneously coupled to light reflected off its surface. The radio-frequency signals are detected as an optical phase shift with quantum-limited sensitivity. The corresponding half-wave voltage is in the microvolt range, orders of magnitude less than that of standard optical modulators. The noise of the transducer--beyond the measured 800 pV Hz-1/2 Johnson noise of the resonant circuit--consists of the quantum noise of light and thermal fluctuations of the membrane, dominating the noise floor in potential applications in radio astronomy and nuclear magnetic imaging. Each of these contributions is inferred to be 60 pV Hz-1/2 when balanced by choosing an electromechanical cooperativity of ~150 with an optical power of 1 mW. The noise temperature of the membrane is divided by the cooperativity. For the highest observed cooperativity of 6,800, this leads to a projected noise temperature of 40 mK and a sensitivity limit of 5 pV Hz-1/2. Our approach to all-optical, ultralow-noise detection of classical electronic signals sets the stage for coherent up-conversion of low-frequency quantum signals to the optical domain.

No abstract

Squeezing of quantum fluctuations by means of entanglement is a well-recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between 2-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for 10 5 cold caesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximizes the generated entanglement. A 2-color QND scheme used in this paper is shown to have a number of advantages for entanglement generation as compared with a single-color QND measurement. N A for the case of independent atoms also referred to as a coherent spin state (CSS). The CSS minimizes the Heisenberg uncertainty product so that, e.g., (δJ z ) 2 (δJ x ) 2 = 1 4| J y | 2 where J y is the expectation value of the spin projection operator. At the expense of an increase in (δJ x ) 2 , it is possible to reduce (δJ z ) 2 (or vice versa) below the projection noise limit while keeping their product constant. This constitutes an example of a spin squeezed state (SSS), for which the atoms need to be correlated. This correlation is ensured to be nonclassical ifwhere ξ defines the squeezing parameter. Under this condition, the atoms are entangled (3) and the prepared state improves the signal-to-noise ratio in spectroscopical and metrological applications (1). Systems of 2 to 3 ions have successfully been used to demonstrate spectroscopic performance with reduced quantum noise and entanglement (4, 5). The situation is somewhat different with macroscopic atomic ensembles where spin squeezing has been an active area of research in the past decade (6-13). To our knowledge, no results reporting ξ < 1 via interatomic entanglement in such ensembles have been reported so far, with a very recent exception of the paper (14) where entanglement in an external motional degree of freedom of 2 · 10 3 atoms via interactions in a Bose-Einstein condensate is demonstrated. Spin Squeezing by Quantum Nondemolition (QND) MeasurementsIn this article, we report on the generation of an SSS fulfilling Eq. 1 in an ensemble of ≈10 5 atoms via a QND measurement (7, 15-17) of J z . We show how to take advantage of the entanglement in this mesoscopic system by using Ramsey spectroscopy (1)-one of the methods of choice for precision measurements of time and frequency (18) (Fig. 1A). The figure presents the evolution of the pseudospin J whose tip is traveling over the Bloch sphere. The Ramsey method allows using the atomic ensemble as a sensor for external fields where the perturbation of the energy difference between the levels ΔE ↑↓ is measured, or as a clock where the frequency of an oscillator is locked to the transition frequency between the two states Ω = ΔE ↑↓ / . Fig. 1 B illustrates how a suitable SSS can improve the precision of the Ramsey measurement pr...

We produce a 600-ns pulse of 1.86-dB squeezed vacuum at 795 nm in an optical parametric amplifier and store it in a rubidium vapor cell for 1 mus using electromagnetically induced transparency. The recovered pulse, analyzed using time-domain homodyne tomography, exhibits up to 0.21+/-0.04 dB of squeezing. We identify the factors leading to the degradation of squeezing and investigate the phase evolution of the atomic coherence during the storage interval.

Abstract. We use a quantum non-demolition measurement to generate a spin squeezed state and to create entanglement in a cloud of 10 5 cold cesium atoms. For the first time we operate an atomic clock improved by spin squeezing beyond the projection noise limit in a proof-of-principle experiment. For a clockinterrogation time of 10 µs, the experiments show an improvement of 1.1 dB in the signal-to-noise ratio, compared to the atomic projection noise limit.

A single photon, delocalized over two optical modes, is characterized by means of quantum homodyne tomography. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical quantum bit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments.PACS numbers: 03.65. Wj, 03.65.Ud, 03.67.Mn, 42.50.Dv According to Feynman, single-particle interference is "a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has it in the heart of quantum mechanics" [1]. The explanation offered by quantum mechanics is that a particle incident onto a beam splitter is not, as classically expected, randomly reflected or transmitted, but forms a delocalized coherent superposition of these two possibilities. The quantum state in the two beam splitter output modes A and B can be expressed aswhere τ 2 and ρ 2 are, respectively, the beam splitter transmission and reflectivity, and the kets in the right-hand side are written in the particle-number basis.In this article, we investigate the delocalized state formed by a photon. We employ homodyne tomography, a state characterization technique based on phase-sensitive measurements of the electromagnetic field quadratures. Although there is only one light particle, we find it to affect the field in both modes simultaneously, giving rise to nonclassically correlated, phase-dependent quadrature statistics. This is a direct consequence of the coherent, entangled nature of the state (1) and is remarkable because the optical phase in both the single-photon and vacuum states considered individually is completely uncertain.We show that the delocalization of the photon in the state (1) can be formulated as a noncontextual violation of local realism, namely as a violation of Bell's inequality [2]. Nonlocality of the single photon has been discussed earlier in a number of theoretical publications, and various experiments were proposed for its demonstration [3] none of which have so far been realized. The present work achieves this goal by using a very different measurement method and by introducing an assumption which resembles the fair sampling assumption in traditional experiments on nonlocality [4]. To our knowledge, this is the first experimental verification of Bell's theorem performed in a continuous-variable setting.Apart from its fundamental implications, our experiment finds its use in the linear optical implementation of quantum optical information processing [5], in which the state (1) plays the role of a quantum bit. To date, characterization of optical qubits has been based on studying relative photon number statistics in each mode and in their various linear superpositions as well as (in the case of multiple qubits) photon number correlations between modes. Employing this approach, White et al. have implemented tomo...

We present the first experimental realization of coherent Bragg scattering off a one-dimensional system-two strings of atoms strongly coupled to a single photonic mode-realized by trapping atoms in the evanescent field of a tapered optical fiber, which also guides the probe light. We report nearly 12% power reflection from strings containing only about 1000 cesium atoms, an enhancement of 2 orders of magnitude compared to reflection from randomly positioned atoms. This result paves the road towards collective strong coupling in 1D atom-photon systems. Our approach also allows for a straightforward fiber connection between several distant 1D atomic crystals.

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance -14  dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of ±8  atoms on an ensemble of some 10(3)  atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.