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arXiv:1307.6364 · Physical Review Letters

Experimentally Accessing the Optimal Temporal Mode of Traveling Quantum Light States

Olivier Morin, Claude Fabre, Julien Laurat

Published Nov 19, 2013• 86 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.111.213602

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•Jan 1, 2014•0 citations
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.
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 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.
Precise information about the temporal mode of optical states is crucial for optimizing their interaction efficiency between themselves and/or with matter in various quantum communication devices. Here we propose and experimentally demonstrate a method of determining both the real and imaginary components of a single photon's temporal density matrix by measuring the autocorrelation function of the photocurrent from a balanced homodyne detector at multiple local oscillator frequencies. We test our method on single photons heralded from biphotons generated via four-wave mixing in an atomic vapor and obtain excellent agreement with theoretical predictions for several settings. A convenient scheme for characterizing the temporal properties of a single photon looks set to aid experiments in quantum optics. An international team of scientists from Canada, China, USA, Uruguay and Russia says that this approach can be used to determine the complete mode structure of a photon, in particular, the real and imaginary parts of its temporal density matrix. This information is important for quantum communication experiments for which it is often critical to match photon modes. The characterization scheme, which the researchers term polychromatic optical heterodyne tomography, works by collecting autocorrelation data of homodyne photocurrent at multiple local oscillator frequencies. The team says that tests of the technique with single photons generated by four-wave mixing in an atomic vapour agree well with theoretical predictions.
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.
Abstract Recent progress in ultrafast optics facilitates the investigation of the dynamics of highly multimode quantum states of light. Yet, the complete tomographic reconstruction of optical quantum states with prior unknown statistics and dynamics is still challenging, since state-of-the-art tomographic methods require the measurement of orthogonal and distinguishable modes. Here, we propose a tomography scheme based on time-domain quadrature correlation measurements and theoretically demonstrate its ability to reconstruct highly multimode Gaussian states. In contrast to (eight-port) homodyne detection, the two local oscillator pulses are shorter in time and are (independently) time-delayed against the pulsed quantum state. The distinguishable mode structure is obtained in post-processing from the correlation measurement data by orthogonalization. We show that the number of reconstructable modes increases with the number of time delays used and decreases with the temporal extent of the local oscillator. Additionally, we compare dual-pulse homodyne detection and electro-optic sampling. By analysing the (quantum) correlations present in the measurement data, we show how thermalisation of the quantum state during detection leads to the requirement of correlation measurements. Furthermore, we open an avenue to extending our tomography scheme to non-Gaussian states.
This thesis is concerned with the generation of non-classical quantum states of light, the photon-level manipulation of quantum states and the accurate tomography of both quantum states and quantum processes. In optics, quantum information can be encoded and processed in both discrete and continuous variables. Hybrid approaches combining for example homodyne detection with conditional state preparation and manipulation are gaining increasing prominence. The development and characterization of a time-domain balanced homodyne detector (BHD) is presented. The detector has a bandwidth of 80 MHz, a signal-to-noise ratio of 14.5 dB and an efficiency of 86% making it well-suited to pulse-to-pulse measurement of quantum optical states. The BHD is employed to perform quantum state tomography (QST) of non-classical multi-photon Fock states generated by spontaneous parametric down-conversion. A detailed investigation of the mode-matching between the local oscillator used for homodyne detection and the generated Fock states is presented. The one-, two- and three-photon Fock states are reconstructed with a combined preparation and detection efficiency exceeding 50%. Fock states have a number of applications in quantum state engineering, where non-classical ancilla states and conditional measurements enable photon-level manipulation of quantum states. Fock state filtration (FSF) is investigated - an example of a post-selected beam splitter which is a basic building block for many quantum state engineering protocols. A model is developed incorporating the effect of experimental imperfections. An experimental implementation of a Fock state filter is fully characterized by means of coherent-state quantum process tomography (QPT). The reconstructed process is found to be consistent with the model. The filter preferentially removes the single-photon component from an arbitrary input quantum state. Calibration of optical detectors in the quantum regime is discussed. Quantum detector tomography (QDT) is reviewed and contrasted with a new technique for performing QST with a calibrated detector known as the fitting of data patterns (FDP). The first experimental characterization of a BHD is performed by probing the detector with phase-averaged coherent states. The FDP method is shown to be applicable to the estimation of quantum processes, where a detector response is not assumed - thus demonstrating the versatility of the FDP approach as a new method in the quantum tomography toolbox.