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.
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.
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.
Characterization of quantum states and detectors is a key task in rapidly emerging optical quantum science and technology. First, we introduce and experimentally demonstrate a noise-robust quantum state characterization protocol using photon-number-resolving (PNR) measurements. Unlike conventional continuous variable state tomography methods, our method utilizes computationally efficient semi-definite programming (SDP) and can be used to accurately reconstruct the state even after loss a known loss. The protocol is demonstrated for a weak coherent state as well as a single-photon Fock state.
Next, we propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector’s Positive-Operator-Value-Measure (POVM) elements via weak-field homodyne technique. We also report our experimental progress on characterizing a superconducting transition-edge sensor for PNR measurements.
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.
The implementation of optical quantum technologies requires precise and complete characterisation tools for multi-mode nonclassical states of light. In this thesis, we propose and we implement experimentally three applications of optical quantum measurements, which combine aspects of light that are described by both discrete and continuous variables. In the rst part of this thesis, we present a new scheme for interferometric phase estimation, which uses double homodyne measurements as an alternative to photon counting. We show that, without requiring a phase reference, this scheme can achieve the optimum phase estimation precision for all path-symmetric probe states with a de ned number of photons. Furthermore, the estimation procedure is robust against state preparation imperfections, and naturally yields the same precision for all values of the estimated phase. We implement the proposed scheme experimentally, using a polarisation interferometer probed by a single-photon signal, and temporally multiplexing a single homodyne detector. We repeat the experiment with classical probe states. For both cases, we demonstrate the accuracy and precision of the proposed method, our implementation deviating by 5% from the fundamental precision bound. We demonstrate that, in our scheme, single-photon probe states can provide better precision than weak coherent ones. These results indicate that hybrid quantum resources, which combine tools from the discrete and continuous-variable paradigms, can play a signi cant role in practical sensing scenarios. In the second part of this thesis, we present an application in the eld of information thermodynamics, reporting an experimental realisation, in a photonic setup, of Maxwell's demon. We show that a measurement at the few-photons level, followed by a feed-forward operation, allows the extraction of work from intense thermal light into an electric circuit. The interpretation of the experiment leads us to the derivation of an equality relating work extraction to information acquired by measurement. We prove a bound using this relation, and show that it is in agreement with the experimental results. Our work puts forward photonic systems as a platform for experiments in the eld of information thermodynamics. In the third part of this thesis, we present a new method for the characterisation of broadband parametric down-conversion, based on stimulated frequency generation. In particular, we analyse the information contained in the frequency generation produced in the same mode as a seeding beam, for a type-II down-conversion process. We derive a model for this signal and argue that its detection can provide a useful characterisation tool in the high-gain regime, allowing for a self-referenced estimation of squeezing gain. We propose a method for measuring this signal and present an experimental realisation, based on a wave-guided source, at telecommunication wavelengths. Our experimental results demonstrate that the proposed measurement is an e ective experimental handle for discerning the intricate structure of broadband parametric down-conversion.
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.
The research activities described in this thesis have basically an experimental profile, and were realized in the Quantum Optics Laboratories of the Optic Division in the Istituto Nazionale di Ricerca Metrologica (I.N.Ri.M.). The experiments presented here are oriented to the characterization of single- and few-photon detectors calibration, exploiting quantum properties. The first chapter has an introductory character, oriented to the study of nonlinear optics phenomena and focused in the spontaneous parametric down conversion (PDC) process. After the quantization of the free electromagnetic field, we recall the quantum theory of PDC. In the second chapter the Klyshko's two-photon calibration technique is presented and applied to an Avalanche Photo Diode (APD) based single photon counting module. Chapter three is an introduction to quantum measurements and quantum operation theories where the concept of positive-operator valued measurement (POVM) is presented. In chapter four, the quantum characterization of a true photon-number resolving detector (PNRD) based on a transition edge sensor (TES) is presented. In this experiment, the POVM of the TES is reconstructed by realizing a tomography of the detection process's quantum operation, using as a probe a set of known coherent states. In the fifth and last chapter, the POVM of a tree type PNRD is reconstructed exploiting strong quantum correlations of PDC twin beams