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Conditional Measurements in Quantum Optics for Application in Quantum Information

Final Report Summary - QUANTMANIP (Conditional Measurements in Quantum Optics for Application in Quantum Information)

The project QuantManip has been devoted to the generation of highly non classical states of the light by manipulation of states of light with quantum noise characterized by a Gaussian distribution. More specifically, the major aim of the project was the experimental realization of quantum states of light obtained as the superposition of two classically distinguishable states, the so-called “cat-states” and realized by subtracting one photon to a squeezed state generated by an optical parametric oscillator (OPO) below threshold. In experiments, the photon subtraction is heralded by a photon counting operation; each time the photon counter detects a photon, a logic gate allows the cat-state to be detected. This scheme is reported as conditional measurement.

When the project started, the OPO source and the homodyne detector, required to measure the state properties, were already mounted at the host laboratory and their functioning was well mastered and understood by all the group members. What had to by done was to implement the entire conditional measurement scheme. This work included the development and mastering of a filtering system on the photon subtraction channel, the photons counting detector itself and the data analysis codes.
The OPO source was a continuous wave (CW) one, generating light naturally multimode and without any intrinsic time binning. In this case the standard single photon detector had be combined with an accurate filtering stage, able to select only the photons relevant to the measurement. During her first year at the Laboratoire Kastler Brossel, Virginia D’Auria worked on the problem of photons filtering, with the objective of obtaining at the same time a filter transmission as high as possible together with the narrowest frequency selectivity. She solved the problem by designing a very compact system, based on the combination of a narrow band interferential filter and a high finesse cavity. This task has demanded a preliminary study relying on numerical simulations, as well as the design of all mechanical components required for the implementation of the, ultra short and ultra stable, optical cavity. The whole setup, including the electronic interface required to servo-assist the cavity, has been assembled, aligned and tested. The overall transmission has been measured to be around 80% in good agreement with what expected. In order to lock the cavity on its maximum transmission despite mechanical vibrations, an additional bright auxiliary beam, with properties as similar as possible to those of the photons to be detected, is required. During the first months of her second year of post-doc, Virginia D’Auria has worked to the problem of locking the filtering cavity (the locking electronics having been already realized during the first year), without directing the strong auxiliary beam toward the single photon counter. The problem has been solved by means of a scheme based on the use of fibred optical switches introducing two time bins; one time bin, in which the auxiliary beam was blocked, was dedicated to the measurements and the other one, in which the detector was blocked and the auxiliary beam enabled, to the cavity locking. This scheme as required a long work of alignment of the time bins in order to guarantee at a most robust locking while keeping the detection windows as long as possible.
The photon counting operation has been performed by means of a superconducting single photon detector (SSPD). Despites standard avalanche photodiodes, this detector provides a good efficiency (16% @ 1064nm) together with a very low dark count (1Hz). However, since the SSPD operation involves a cryogenic environment, its manipulation has demanded to acquire competences in this sense. During her first year of post-doc, Virginia D’Auria has learnt how to employ the SSPD detector and to accurately characterized its performances, in terms of quantum efficiency and dark count for different working conditions and wavelengths (at 1064nm in CW and at 800nm with a femtoseconds pulsed laser). A possible implementation of SSPDs for photon number resolving has been studied in the frame of a collaboration with the CEA laboratory in Grenoble. Concerning the data analysis, Virginia D’Auria has combined her experimental activity with theoretical and numerical work. More specifically she has developed a program (under mathematica and matlab platform) aiming to tomographically reconstruct the cat-state properties by means of homodyne date. The code has successfully been tested with data relative to the detection a squeezed states, and later on, on preliminary measurement of the Schrödinger cat.

As stated before, in conditional measurements on quantum-correlated photons, the detection of a single-photon on one of the beam heralds the generation of a single-photon state or of a Schrödinger cat on the other one. Such a scheme requires a precise knowledge of the heralding detector properties, such as its efficiency, its noise or its photon-number resolution ability. These performance parameters strongly affect the preparation rate and the fidelity of the generated state.
This context has led to a work concerning the behaviour of quantum photon detectors. The experiment has been mostly performed during the second year of post-doctoral activity of Virginia D’Auria.
The basic idea was to evaluate the effects of detector properties on conditional preparation and to compare two kinds of detectors; a conventional on/off detector and a time multiplexed one. To this aim, Virginia D’Auria has designed and entirely assembled a dedicated experiment, employing for the characterization a femtoseconds pulsed source at 800nm. The photon-detectors have been characterized by registering their response to a specific class of quantum states, whose quantum properties were known in advance. This technique is generally known as the quantum detector tomography. Provided the number of test states is large enough, it is possible to obtain, from the collection of the detector outputs, the probability pi with whom it will deliver the response “i”, when stimulated with any quantum state. In the experiment, the on/off detector was a conventional avalanche photodiode (APD), able only to tell if “at least” one photon has been detected (on) or not (off). The photon number resolving detector was realized by time multiplexing the light toward two optical path, with one of the path introducing a delay ∆T with respect to the other. The two paths are eventually recombined and sent to an APD. The arrival of two photons will correspond to two subsequent clicks, spaced of ∆T thus giving rise to three possible responses: off, 1 click, 2 clicks. Beside the optical realization, this work has required a specific electronic interface, consisting of logic gates well adapted to match the detection time windows with the femtosecond laser pulses; Virginia D’Auria has entirely realized the demanded electronic equipment.
The detector background noise level has been changed in a controlled way; an extra noise with Poissonian statistics has been introduced by sending to the detector, together with the test states an additional laser beam (CW @1064nm) with a well-determined mean photon number. The so-called decoherence effects of detector, induced by dark counts, have been observed. As for the cat-state generation, Virginia D’Auria has autonomously elaborated a program (under Mathematica platform) exploiting a maximum likelihood algorithm to reconstruct the detector properties.
Besides the purely experimental work, Virginia D’Auria has worked on the theoretical modelling of the detectors under estimation. In a second time, she used the experimental data on detector tomography, in combination with a theoretical model simulating a typical entangled state, to evaluate the effect of detector dark count on conditional preparation of single photon state. The detector decoherence work and the study of the effect of noisy detector in conditional preparation of single photon state are the objects of two papers respectively submitted and in preparation.