Summary form only given. We find that the quantum statistics of multimode squeezed fields are easily obtained and simply understood via an eigenmode description. The eigenmode description of squeezed light is based on our finding that the squeezing matrix /spl Gamma/ can always be diagonalized by a physical transformation of the fields - either a change of basis or linear unitary evolution. Each eigenmode possesses single-mode squeezing statistics, and the corresponding eigenvalue is the effective squeezing parameter for that mode. The squeezing eigenmodes are completely uncoupled from one another (at the quantum level) and represent independent channels (pixels) useful for carrying noise-sensitive data. We show how an eigenmode description of a squeezed field allows one to easily calculate noise statistics of the field upon diffraction and/or propagation through any sequence of lossless linear optical elements. We further show that the eigenmodes define the shape of the local oscillator which must be used in order to obtain the smallest quantum noise in balanced homodyne or heterodyne measurements. Finally, we use the theory to model pulsed optical parametric downconversion in a /spl chi//sup (2)/ medium with a classical pump field of arbitrary bandwidth, allowing for the possibility of phase and/or group velocity mismatch.
Summary form only given. We find that the quantum statistics of multimode squeezed fields are easily obtained and simply understood via an eigenmode description. The eigenmode description of squeezed light is based on our finding that the squeezing matrix /spl Gamma/ can always be diagonalized by a physical transformation of the fields - either a change of basis or linear unitary evolution. Each eigenmode possesses single-mode squeezing statistics, and the corresponding eigenvalue is the effective squeezing parameter for that mode. The squeezing eigenmodes are completely uncoupled from one another (at the quantum level) and represent independent channels (pixels) useful for carrying noise-sensitive data. We show how an eigenmode description of a squeezed field allows one to easily calculate noise statistics of the field upon diffraction and/or propagation through any sequence of lossless linear optical elements. We further show that the eigenmodes define the shape of the local oscillator which must be used in order to obtain the smallest quantum noise in balanced homodyne or heterodyne measurements. Finally, we use the theory to model pulsed optical parametric downconversion in a /spl chi//sup (2)/ medium with a classical pump field of arbitrary bandwidth, allowing for the possibility of phase and/or group velocity mismatch.
We analyze the output of a degenerate optical parametric amplifier using a different approach to understanding and characterizing multimode squeezed light. This approach is based on the concept of eigenmodes of the squeezing and predicts the mode structure of the local oscillator that should be used in order to measure the smallest quadrature noise. Although the importance of mode matching is well known, we find that typical experimental setups are suboptimal and we predict that in such cases squeezed light measurements stand to be improved noticeably with appropriate shaping (in space and/or time) of the local oscillator field in accordance with the results of the theory. Under conditions of negligible or small phase mismatch, the optimal local oscillator pulse duration is found to be approximately equal to the geometric mean of the pump pulse duration and nonlinear response time. Also, we find that the effective number of squeezed modes can be altered by varying the pump pulse duration and/or phase-matching parameters.
Optical parametric amplifiers (OPAs) configured as phase-sensitive amplifiers (PSAs) can be used for noiseless optical image amplification, generation of non-classical states of light, and, in particular, for multimode squeezed light generation. For all these applications and for effective use of the quantum properties of the multimode PSA, we need to know its independently squeezed (or amplified) eigenmodes. First we present the quantum theory of a spatially multimode traveling-wave PSA pumped by a high-power pump beam with arbitrary spatial profile. To quantitatively identify the Green's function of the PSA, we have developed a semi-analytical coupled-mode-theory of the PSA using 2D Hermite-Gaussian mode expansions of the signal- and pump-beam spatial distributions. By using Green's functions of the classical OPA, we calculate the normallyordered quadrature correlators at its output, which provide complete quantum description of the phase-sensitive OPA and enable determination of its independently squeezed eigenmodes. We find the number of the supported eigenmodes and their shapes for a spatially broadband frequency-degenerate optical parametric amplifier with elliptical Gaussian pump. We conclude by discussing our recent extensions of the coupled-mode-theory to study higher-order pump modes, compact representation of the PSA eigenmodes (especially convenient for experiments), and effect of non-zero phase mismatch on the PSA eigenmodes. We expect that the results from our model can be used for optimum mode matching in phase-sensitive image amplification and multimode squeezing generation.
We analyze the spectral properties of squeezed light produced by means of pulsed, single-pass degenerate parametric down-conversion. The multimode output of this process can be decomposed into characteristic modes undergoing independent squeezing evolution akin to the Schmidt decomposition of the biphoton spectrum. The main features of this decomposition can be understood using a simple analytical model developed in the perturbative regime. In the strong pumping regime, for which the perturbative approach is not valid, we present a numerical analysis, specializing to the case of one-dimensional propagation in a beta-barium borate waveguide. Characterization of the squeezing modes provides us with an insight necessary for optimizing homodyne detection of squeezing. For a weak parametric process, efficient squeezing is found in a broad range of local oscillator modes, whereas the intense generation regime places much more stringent conditions on the local oscillator. We point out that without meeting these conditions, the detected squeezing can actually diminish with the increasing pumping strength, and we expose physical reasons behind this inefficiency.
Nowadays, the realization of quantum computations and communications based on continuous variables has attracted a significant attention due to a substantial expansion of the system dimensionality. The main progress in this area is attributed to the implementation of multimode systems based on squeezed states of light. One of the simplest ways to generate such states relies upon their producing in a single-pass optical parametric amplifier (OPA) using ultrafast pumping. However, for homodyne detection of such multimode states, the profile of the local oscillator (LO) must perfectly match the profile of the measured mode. Usually, this is not the case; therefore a proper treatment of multimode squeezing is required. In this work, we study both theoretically and experimentally the multimode squeezed light generated in type-0 and type-II OPA. We characterize such sources and investigate the degree of squeezing in dependence on the LO spectral profile, employing a pulse shaping technique. The theoretical analysis is performed using the Schmidt-mode theory. This work might have a significant impact on the realization of multimode quantum protocols
Multimode squeezed light is an increasingly popular tool in photonic quantum technologies, including sensing, imaging, and computation. Meanwhile, the existing methods of its characterization are technically complicated, which reduces the level of squeezing, and mostly deal with a single mode at a time. Here, for the first time, to the best of our knowledge, we employ optical parametric amplification to characterize multiple squeezing eigenmodes simultaneously. We retrieve the shapes and squeezing degrees of all modes at once through direct detection followed by modal decomposition. This method is tolerant to inefficient detection and does not require a local oscillator. For a spectrally and spatially multimode squeezed vacuum, we characterize eight strongest spatial modes, obtaining squeezing and anti-squeezing values of up to −5.2 ± 0.2 dB and 8.6 ± 0.3 dB, respectively, despite the 50% detection loss. This work, being the first exploration of an optical parametric amplifier’s multimode capability for squeezing detection, paves the way for the real-time detection of multimode squeezing.
When light scatters from an object, it can impart some physical quantity such as momentum or angular momentum. This can act as a measurement on the photon, which collapses on to an eigenstate of the measurement operator. However the corresponding operator is not the same as that describing the total linear or angular momentum in free space. Optical eigenmodes provide a powerful method to describe this interaction by expanding the field as a linear combination of some basis modes and examining the eigenvalues and eigenvectors of the quadratic measure in question. We extend this to the quantum case by writing the quantum operator corresponding to a given measurement such as energy, momentum or angular momentum as a superposition of creation and annihilation operators for each eigenmode. Upon measurement we find that the possible states of a single photon are simply the classical eigenmodes of the measurement. As an application, we examine the force and torque on a general, possibly anisotropic, material. By looking at eigenvalues of the measurement operator we show that the amount of a given quantity transferred in an interaction with matter is not in general the expected amount which a photon carries in free space, even at the single photon level. In particular the difference in linear or angular momentum from before and after is in general not equal to ~k or ~ which are the eigenvalues of these quantities in free space.