Matter-light quantum interface and quantum memory for light are important ingredients of quantum information protocols, such as quantum networks, distributed quantum computation, etc. ͓P. Zoller et al., Eur. Phys. J. D 36, 203 ͑2005͔͒. In this paper we present a spatially multimode scheme for quantum memory for light, which we call a quantum hologram. Our approach uses a multiatom ensemble which has been shown to be efficient for a single spatial mode quantum memory. Due to the multiatom nature of the ensemble and to the optical parallelism it is capable of storing many spatial modes, a feature critical for the present proposal. A quantum hologram with the fidelity exceeding that of classical hologram will be able to store quantum features of an image, such as multimode superposition and entangled quantum states, something that a standard hologram is unable to achieve.

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We propose a new scheme for parallel spatially multimode quantum memory for light. The scheme is based on counter-propagating quantum signal wave and strong classical reference wave, like in a classical volume hologram, and therefore can be called a quantum volume hologram. The medium for the hologram consists of a spatially extended ensemble of atoms placed in a magnetic field. The write-in and read-out of this quantum hologram is as simple as that of its classical counterpart and consists of a single pass illumination. In addition we show that the present scheme for a quantum hologram is less sensitive to diffraction and therefore is capable of achieving higher density of storage of spatial modes as compared to previous proposals. A quantum hologram capable of storing entangled images can become an important ingredient in quantum information processing and quantum imaging.

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We investigate the nonstationary and relaxation phenomena in cavityassisted quantum memories for light. As a storage medium we consider an ensemble of cold atoms with standard Lambdascheme of working levels. Some theoretical aspects of the problem were treated previously by many authors, and recent experiments stimulate more deep insight into the ultimate ability and limitations of the device. Since quantum memories can be used not only for the storage of quantum information, but also for a substantial manipulation of ensembles of quantum states, the speed of such manipulation and hence the ability to write and retrieve the signals of relatively short duration becomes important. In our research we do not apply the socalled bad cavity limit, and consider the memory operation of the signals whose duration is not much larger than the cavity field lifetime, accounting also for the finite lifetime of atomic coherence. In our paper we present an effective approach that makes it possible to find the nonstationary amplitude and phase behavior of strong classical control field, that matches the desirable time profile of both the envelope and the phase of the retrieved quantized signal. The phase properties of the retrieved quantized signals are of importance for the detection and manipulation of squeezing, entanglement, etc by means of optical mixing and homodyning.

We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently for a cavity-based geometry, such a scheme can amplify images without deteriorating their signal-to-noise ratio thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We study in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. We investigate physical features of noiseless amplification, which take place for both traveling-wave and ring-cavity configurations. We demonstrate how the optimum phase matching of a phase-sensitive wave front of an image ͑by means of a thin lens or a small displacement of the crystal͒ can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the possibility of using detectors with the area much smaller than the area of the input image elements. We compare our results with those obtained for the ring-cavity configuration.image amplification was observed for the first time. The results of our analysis can be useful for experimental research in the field of generation, detection, and amplification of low-noise optical images.The paper is organized as follows: In Sec. II we describe the optical scheme of the traveling-wave parametric amplifier. This scheme is very similar to that of Ref. ͓6͔ where we refer for details. In Sec. III we give a physical explanation of the space-dependent squeezing transformation. Section IV is devoted to investigation of the gain and noise characteristics of the optimized traveling-wave noiseless amplifier. Finally, in Sec. V we demonstrate the effect of the optimum phase matching on the ring-cavity amplifier. The spatial scales and the noise parameters of the traveling-wave and the ringcavity noiseless amplifiers are compared.

We propose a source of multimode squeezed light that can be used for superresolving microscopy. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a Fourier lens. We demonstrate that such an arrangement produces squeezed prolate spheroidal waves that are the eigenmodes of the optical imaging scheme used in microscopy and discuss the conditions of the degree of squeezing and of the number of spatial modes in illuminating light.