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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Optimal temporal mode extraction for quantum state engineering via a direct multimode analysis of homodyne data

Olivier Morin, Claude Fabre, Julien Laurat

Published May 1, 2013• 0 citations
Publisher

Abstract

Summary form only given. The ability to engineer various quantum states of light is a central requirement for quantum information processing, including quantum communication, computing and metrology. In this endeavor, many experiments use the so-called conditional preparation technique. The dynamic of the heralded states, i.e. its temporal mode, mainly depends on the setup and has been studied theoretically with different strategies [1,2]. However, it remains difficult to extract the optimal mode with a precise description of the experimental setup: it requires very often some additional assumptions. This is why it is important to characterize experimentally the dynamic of the generated states as it might improve the fidelity of the generated state.

DOI
10.1109/cleoe-iqec.2013.6801653

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Summary form only given. The ability to engineer various quantum states of light is a central requirement for quantum information processing, including quantum communication, computing and metrology. In this endeavor, many experiments use the so-called conditional preparation technique. The dynamic of the heralded states, i.e. its temporal mode, mainly depends on the setup and has been studied theoretically with different strategies [1,2]. However, it remains difficult to extract the optimal mode with a precise description of the experimental setup: it requires very often some additional assumptions. This is why it is important to characterize experimentally the dynamic of the generated states as it might improve the fidelity of the generated state.
The characterization or subsequent use of a propagating optical quantum state requires the knowledge of its precise temporal mode. Defining this mode structure very often relies on a detailed a priori knowledge of the used resources, when available, and can additionally call for an involved theoretical modeling. In contrast, here we report on a practical method enabling us to infer the optimal temporal mode directly from experimental data acquired via homodyne detection, without any assumptions on the state. The approach is based on a multimode analysis using eigenfunction expansion of the autocorrelation function. This capability is illustrated by experimental data from the preparation of Fock states and coherent state superposition.
Conditional preparation is a well-established technique for quantum state engineering of light. A general trend is to increase the number of heralding detection events in such a realization to reach larger photon-number states or their arbitrary superpositions. In contrast to pulsed implementations, where detections only occur within the pulse window, for continuous-wave light the temporal separation of the conditioning detections is an additional degree of freedom and a critical parameter. Based on a theoretical study by Nielsen and M\o{}lmer [A. E. B. Nielsen and K. M\o{}lmer, Phys. Rev. A 75, 043801 (2007)] and on a continuous-wave two-mode squeezed vacuum from a nondegenerate optical parametric oscillator, we experimentally investigate the generation of two-photon state with tunable delay between the heralding events. The present work illustrates the temporal multimode features in play for conditional state generation based on continuous-wave light sources and quantifies the compromise between preparation rate and fidelity in this scenario.
Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks. A comprehensive framework recently established that broad families of quantum states can attain the Heisenberg limit, surpassing any classical strategy. This raises a fundamental question: among all quantum-enhanced strategies, which is truly optimal? Answering this requires identifying physically meaningful resources governing each estimation task, so quantum states can be compared on equal footing. We show these resources are connected to the eigenmode basis of the generator of the relevant mode transformation. For time-shift estimation, whose generator is diagonal in the frequency domain, the pertinent resources are the mean frequency and bandwidth; analogous quantities emerge for other transformations. Our framework unifies two historically separate perspectives: the particle-number aspect and the mode-structure of quantum light, providing a coherent picture of quantum-enhanced sensing with multimode radiation. Within this unified framework, we derive a tight upper bound on the quantum Fisher information for multimode Gaussian states, expressed in terms of these natural resources, and analytically identify the optimal Gaussian states saturating it. These optimal states take a particularly transparent form in the generator eigenbasis, a structural simplicity reflecting the deep connection between the geometry of the mode transformation and the architecture of the optimal probe. We further demonstrate that multimode homodyne detection constitutes the optimal measurement, achieving this bound and completing the end-to-end characterization of optimal quantum metrology strategies for mode parameter estimation.
The knowledge and thus characterization of the temporal modes of quantum light fields is important in many areas of quantum physics ranging from experimental setup diagnosis to fundamental-physics investigations. Recent results showed how the autocorrelation function computed from continuous-wave homodyne measurements can be a powerful way to access the temporal mode structure. Here, we push forward this method by providing a deeper understanding and by showing how to extract the amplitude and phase of the temporal mode function with reduced experimental resources. Moreover, a quantitative analysis allows us to identify a regime of parameters where the method provides a trustworthy reconstruction, which we illustrate experimentally.
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
Abstract Nowadays the fields of Quantum Optics and Quantum Information are experiencing a mayor development worldwide, in particular, in the experimental arena. The reason relies in the high perspectives of application of these fields in areas as computing, security, telecommunications and metrology, among others. A determinant fact for the experimental and technological development is the ability to design and construct electronic devices suitable for the study of light with quantum features, as well as the software which is necessary for the analysis and processing of experimental data. In this work we present a general overview of the theory, practical design and experimental tests of one of such devices called Homodyne Detector addressed to the study and engineering of quantum states of light.