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arXiv:1908.04765 · Physical Review A

Tuning between photon-number and quadrature measurements with weak-field homodyne detection

Guillaume Thekkadath, D. S. Phillips, Jacob F. F. Bulmer, William R. Clements, A. Eckstein, Bryn A. Bell, Jasleen Lugani, Tom A. W. Wolterink, Adriana E. Lita, Sae Woo Nam, Thomas Gerrits, C. G. Wade, Ian A. Walmsley

Published Mar 20, 2020• 39 citations
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Abstract

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.

DOI
10.1103/physreva.101.031801

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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.
A longstanding goal in quantum optics has been to realize a photon-number-resolving detector that efficiently counts the number of photons in an optical field. This goal has been largely met with the development of transition edge sensors which can count up to roughly 20 photons with efficiencies over 95%. This thesis presents three experiments that employ these detectors to characterize and prepare quantum states of light. Firstly, we develop a weak-field homodyne detector. By replacing the photodiodes conventionally used in homodyne detection with transition edge sensors, we experimentally implement a versatile measurement device that can tune between photon counting and quadrature measurements. We study the transition between these complementary measurement regimes and determine the minimum local oscillator strength needed to perform quadrature measurements. Secondly, we use the weak-field homodyne detector as a quantum state engineering tool. We propose a scheme to prepare a wide range of definite parity states, including two- and four-component Schrödinger cat states of arbitrary size with nearly perfect fidelity. Thirdly, we perform optical interferometry using quantum states of light with the aim of surpassing the maximal precision achievable with classical light, i.e. the shot-noise limit. We propose and experimentally implement a scheme that uses high-gain squeezed vacuum sources and transition edge sensors to prepare loss-tolerant entangled states containing up to 8 photons. While our achieved precision does not unconditionally (i.e. without post-selecting on certain measurement trials) surpass the shot-noise limit, our results do demonstrate the robustness of these entangled states to loss despite their size.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature. In this paper we explore the possibility of operating a conjugate homodyne detection system in ``photon counting'' mode to implement discrete-variable (DV) quantum key distribution (QKD). A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures XXX and PPP of the incoming quantum state. In classical electrodynamics, X2+P2{X}^{2}+{P}^{2}X2+P2 is proportional to the energy (the photon number) of the input light. In quantum optics, XXX and PPP do not commute and thus the above photon-number measurement is intrinsically noisy. This implies that a blind application of standard security proofs of QKD could result in pessimistic performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuations cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number distribution at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a family of QKD protocols, complementary to the well-established DV-QKD based on single-photon detection and CV-QKD based on coherent detection.
The measurement of quantum states of light is fundamental for the investigations of Quantum Optics and for the applications of Quantum Information. Here we present the implementation of a novel detection apparatus, that is a homodyne-like detection scheme based on photon-number-resolving detectors. Thanks to its hybrid nature, the apparatus is useful to investigate both the particle-like and wave-like properties of light. We tested the scheme in the measurement of the quadratures of different optical states, namely coherent states and mixtures of coherent states. In particular, we investigate the performance of our scheme compared to that of a standard homodyne detector.
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.