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

Measuring nonlocal coherence with weak-field homodyne detection

Tim J. Bartley, Gaia Donati, Xian‐Min Jin, Animesh Datta, Marco Barbieri, Ian A. Walmsley

Published May 1, 2013• 0 citations
Publisher

Abstract

A feature of quantum mechanical states is delocalised coherence. We directly observe this coherence up to the three photon level. Explicitly, we carry out two-mode weak-field homodyne of both a single photon split at a beam splitter and a two-mode squeezed state. While our measurements are insufficient to quantify or witness entanglement directly, with improved collection efficiency and measurement stability we aim to show that this can be achieved with such a scheme. Thus we have shown how such a detector can directly probe coherence in both the discrete and continuous variable pictures.

DOI
10.1109/cleoe-iqec.2013.6801631

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A feature of quantum mechanical states is delocalised coherence. We directly observe this coherence up to the three photon level. Explicitly, we carry out two-mode weak-field homodyne of both a single photon split at a beam splitter and a two-mode squeezed state. While our measurements are insufficient to quantify or witness entanglement directly, with improved collection efficiency and measurement stability we aim to show that this can be achieved with such a scheme. Thus we have shown how such a detector can directly probe coherence in both the discrete and continuous variable pictures.
Entangled photons are ideally suited to the transmission of photonic quantum information. Mitigating the effects of decoherence is fundamental to distributing photonic entanglement across large distances. One such proposal is entanglement distillation, in which operations on a large ensemble of weakly entangled states generate a smaller ensemble of more strongly entangled states. In this thesis, we experimentally and theoretically analyse various tools required for demonstrating continuous-variable (CV) entanglement distillation, following the proposal by Browne et al., [Phys. Rev. A 67, 062320 (2003)]. Specifically, we propose figures of merit to account for the practical limitations of non-deterministic non-Gaussian operations, and analyse the experimental parameters necessary to optimise them. We develop a source of pulsed two-mode squeezed states, which are the initial states of our entanglement distillation protocol. We use weak-field homodyne detection as a phase-dependent photon counting detector, and demonstrate its utility in conditional state generation. Using these states, we demonstrate sub-binomial light as a tool for benchmarking quantum states. Finally, we applied two-mode weak-field homodyne detection to two entangled states and demonstrate correlations in the photon counting statistics which depend on a joint phase from two independent local oscillators. This setup is sufficient to apply an entanglement witness developed by Puentes et al. [New J. Phys. 12, 033042 (2010)]. Despite encouraging simulations, we do not witness entanglement with this scheme, which we attribute to a noise source unaccounted for in the simulations. Although we do not demonstrate entanglement distillation outright, the tools we develop to do so represent a general, hybrid approach to CV quantum optics. Developing tools such as phase-resolved projective measurement on two-mode states allows us to probe both the wave and particle nature of entangled light at the single-photon level. Using and expanding these techniques to probe larger quantum systems may prove useful in studies of fundamental physics and quantum enhanced technologies.
Quantum correlations play a fundamental role in quantum information science. The variety of their manifestations has become increasingly apparent following the development of novel light sources, protocols and photodetectors. One broad classification identifies two instances of non-classical correlations: particle and mode entanglement. These categories mirror two coexisting descriptions of quantum systems in terms of discrete and continuous variables of the electromagnetic field. The past decades have generated a number of promising results based on schemes which encompass elements from both frameworks, rather than viewing the two descriptions as mutually exclusive. In this context, it is possible to conceive and realise experiments where either the quantum resource or the detection system is 'hybrid'. Optical weak-field homodyne detectors bring together phase sensitivity and photon counting; as such, they represent a detection scheme which works across continuous and discrete variables of the radiation field. In this thesis we present a two-mode weak-field homodyne detection layout with added photon-number resolution and apply it to the study of a split single-photon state and a squeezed vacuum state. As a first test of the capabilities of this system, we investigate the reconstruction of relevant features of a given quantum resource - such as its photon statistics - with our detection scheme. Further, we experimentally demonstrate the observation of an instance of non-classical optical coherence which combines the continuous- and discrete-variable descriptions explicitly. The ability to probe phenomena at the interface of wave and particle regimes opens the way to novel, improved schemes for quantum information processing. From a more fundamental perspective, such hybrid approaches may shed light on the very roots of quantum enhancement.
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coherent state amplitude. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector.
We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.
Following a recent theoretical proposal [J. Fiur\'a\ifmmode \check{s}\else \v{s}\fi{}ek and N. J. Cerf, Phys. Rev. Lett. 93, 063601 (2004)], we experimentally implement a scheme to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. The suggested setup is based on only a tunable beam splitter and a direct single-photon detector to fully characterize the generated Gaussian states. We discuss the experimental implementation of this procedure and compare it to other reference methods. A detailed exploitation of our results highlights some practical limitations of this method. This experimental work is followed by a detailed numerical analysis to derive the conditions required for the procedure to succeed. In particular, it is found that an overall single-photon detection efficiency of about 50% is needed, which is difficult to achieve in the present experiment.
The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such a process involves the coupling of a single system of interest, called signal, with a single probe system, so that the relevant information in the signal system is indirectly measured by observing the probe system. Here we extend the concept of quantum nondemolition interaction to the cases in which the signal and the probe systems are each one multipartite continuous-variable system. Specifically, we propose a general scheme that performs the multipartite QND interactions, relying on beam-splitter couplings between the signal and probe modes with only two ancillary modes prepared offline in squeezed states. The scheme is also composed of homodyne detection and feedforward modulation. The ancillary modes are detected in the process, providing photocurrents for postmodulation of the output systems, as well as sufficient information to calculate genuine multipartite entanglement conditions of the input systems and to monitor similar conditions of the output systems.