We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian states. We apply the formula to the problems of estimating phase, purity, loss, amplitude, and squeezing. In the case of the simultaneous measurement of several parameters, we provide the full quantum Fisher information matrix. Our results unify previously known partial results, and constitute a complete solution to the problem of knowing the best possible sensitivity of measurements based on a single-mode Gaussian state

Multimode Gaussian quantum light, which includes multimode squeezed and multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications in quantum information processing and metrology. In this paper, we determine the ultimate sensitivity in the estimation of any parameter when the information about this parameter is encoded in such light, irrespective of the information extraction protocol used in the estimation and of the measured observable. In addition we show that an appropriate homodyne detection scheme allows us to reach this ultimate sensitivity. We show that, for a given set of available quantum resources, the most economical way to maximize the sensitivity is to put the most squeezed state available in a well-defined light mode. This implies that it is not possible to take advantage of the existence of squeezed fluctuations in other modes, nor of quantum correlations and entanglement between different modes.

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example in cluster state computation. We report in this paper the first experimental evidence of a multimode non-classical frequency comb in a femtosecond synchronously pumped optical parametric oscillator. In addition to a global reduction of its quantum intensity fluctuations, the system features quantum correlations between different parts of its frequency spectrum. This allows us to show that the frequency comb is composed of several uncorrelated eigenmodes having specific spectral shapes, two of them at least being squeezed, and to characterize their spectral shapes.PACS numbers: 42.50. Dv, 42.50.Lc, 42.65.Yj Optical frequency combs are perfect tools for high precision metrological applications [1,2]. The extension of their extraordinary properties to the quantum domain may lead to significant progress in different areas of quantum physics, in particular in quantum metrology and parameter estimation [3,4], but also in quantum computation with continuous variables [5,6]. Indeed, one of the main challenges of experimentally implementing quantum computers in the continuous variable regime, for example in cluster state computation [6,7], is the generation of highly multimode non-classical states of light, and the scalability of this generation. As the difficulty of linearly mixing distinct squeezed light sources [8,9] increases as the number of modes increases, it can be more interesting to use instead a single highly multimode source which directly produces non-classical resources shared between many modes within a same beam. In this perspective, optical frequency combs, which span over thousands of different frequency modes, are a very promising system for scalable generation of spectral/temporal multimode quantum states. We report in this paper the first experimental evidence of multimode non-classical frequency comb generated by an Optical Parametric Oscillator (OPO) in the femtosecond regime, which opens the way to the generation of these highly multimode states.Multimode non-classical light has been already experimentally generated with spatial multimode beams produced by OPOs [10,11], and very recently, with the longitudinal modes of an OPO [12,13]. In the domain of temporal modes, single mode squeezing of short pulses has been observed in various experiments starting from [14] in the nanosecond regime. Non-classical states of single femtosecond pulses are the subject of many recent studies (for example [15]). Multimode squeezed solitons have been generated in an optical fiber [16]. Single mode quantum noise reduction in picosecond frequency combs has already been achieved with a Synchronously Pumped Optical Parametric Oscillator (SPOPO) [17], which is an OPO pumped by a train of ultrashort pulses that are synchronized with the pulses making round trips inside the optical cavity.It has recently been shown [18,19] that such SPOPOs generate squeezed frequency combs which are multimode. ...

Three-level atomic gradient echo memory ( -GEM) is a proposed candidate for efficient quantum storage and for linear optical quantum computation with time-bin multiplexing [Hosseini et al., Nature (London) 461, 241 (2009)]. In this paper we investigate the spatial multimode properties of a -GEM system. Using a high-speed triggered CCD, we demonstrate the storage of complex spatial modes and images. We also present an in-principle demonstration of spatial multiplexing by showing selective recall of spatial elements of a stored spin wave. Using our measurements, we consider the effect of diffusion within the atomic vapor and investigate its role in spatial decoherence. Our measurements allow us to quantify the spatial distortion due to both diffusion and inhomogeneous control field scattering and compare these to theoretical models.

We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favorable scaling with an increasing number of modes where N memories can be configured to implement arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memories are used to implement a conditional cz gate.

Photon-subtracted and photon-added Gaussian states are amongst the simplest non-Gaussian states that are experimentally available. It is generally believed that they are some of the best candidates to enhance sensitivity in parameter extraction. We derive here the quantum Cramér-Rao bound for such states and find that for large photon numbers photon-subtraction or -addition only leads to a small correction of the quantum Fisher information (QFI). On the other hand a divergence of the QFI appears for very small squeezing in the limit of vanishing photon number in the case of photon subtraction, implying an arbitrarily precise measurement with almost no light. However, at least for the standard and experimentally established preparation scheme, the decreasing success probability of the preparation in that limit exactly cancels the divergence, leading to finite sensitivity per square root of Hertz, when the duration of the preparation is taken into account.

Precise control of atom-light interactions is vital to many quantum information protocols. In particular, atomic systems can be used to slow and store light to form a quantum memory. Optical storage can be achieved via stopped light, where no optical energy remains in the atoms, or as stationary light, where some optical energy remains present during storage. In this work, we demonstrate a form of self-stabilising stationary light. From any initial state, our atom-light system evolves to a stable configuration that is devoid of coherent emission from the atoms, yet may contain bright optical excitation. This phenomenon is verified experimentally in a cloud of cold Rb87 atoms. The spinwave in our atomic cloud is imaged from the side allowing direct comparison with theoretical predictions.Coherent atom light interactions lie at the heart of many quantum information systems [1, 2]. In particular, implementations of quantum repeaters will likely rely on mapping of photonic states onto atomic systems to enable storage of quantum information [3,4]. Deterministic quantum logic gates in optical systems may also rely on atomic state mapping to enable nonlinear photon-photon interactions [5,6,7,8,9]. A fundamental issue facing any attempt to implement nonlinear cross phase modulation (XPM) is that the interaction is inherently very weak. Techniques are therefore required to increase the interaction time or interaction strength to allow useful amounts of phase shift. Interaction strength can be scaled up by choosing a nonlinear medium with strong optical interactions, such as Rydberg atoms [10,11]. A more general approach that works for any medium is to use smaller interaction volumes, since this increases the electric field per photon, and longer interaction times, which may be achieved by using an 1 arXiv:1609.08287v1 [quant-ph]

We propose a direct and real-time displacement measurement using an optical frequency comb, able to compensate optically for index of refraction variations due to atmospheric parameters. This scheme could be useful for applications requiring stringent precision over a long distance in air, a situation where dispersion becomes the main limitation. The key ingredient is the use of a mode-locked laser as a precise source for multi-wavelength interferometry in a homodyne detection scheme. By shaping temporally the local oscillator, one can directly access the desired parameter (distance variation) while being insensitive to fluctuations induced by parameters of the environment such as pressure, temperature, humidity and CO2 content.