A. I. Lvovsky

Continuous-variable optical quantum-state tomography

This review covers latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special accent on its practical aspects and applications in quantum information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics are discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.

Quantum State Reconstruction of the Single-Photon Fock State

We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.

Quantum Memory for Squeezed Light

We produce a 600-ns pulse of 1.86-dB squeezed vacuum at 795 nm in an optical parametric amplifier and store it in a rubidium vapor cell for 1 mus using electromagnetically induced transparency. The recovered pulse, analyzed using time-domain homodyne tomography, exhibits up to 0.21+/-0.04 dB of squeezing. We identify the factors leading to the degradation of squeezing and investigate the phase evolution of the atomic coherence during the storage interval.

Remote preparation of a single-mode photonic qubit by measuring field quadrature noise.

An electromagnetic field quadrature measurement, performed on one of the modes of the nonlocal single-photon state alpha|1,0>-beta|0,1>, collapses it into a superposition of the single-photon and vacuum states in the other mode. We use this effect to implement remote preparation of arbitrary single-mode photonic qubits conditioned on observation of a preselected quadrature value. The preparation efficiency of the resulting qubit can be higher than that of the initial single photon.

Iterative maximum-likelihood reconstruction in quantum homodyne tomography

I propose an iterative expectation maximization algorithm for reconstructing the density matrix of an optical ensemble from a set of balanced homodyne measurements. The algorithm applies directly to the acquired data, bypassing the intermediate step of calculating marginal distributions. The advantages of the new method are made manifest by comparing it with the traditional inverse Radon transformation technique.

High-resolution Doppler-free molecular spectroscopy with a continuous-wave optical parametric oscillator.

We present a reliable, narrow-linewidth (100-kHz) continous-wave optical parametric oscillator (OPO) suitable for high-resolution spectroscopy applications. The singly resonant OPO with a resonated pump is based on periodically poled lithium niobate crystal and features a specially designed intracavity etalon, which permits precise tuning to any desired wavelength in a wide range. We demonstrate Doppler-free spectroscopy of a rovibrational transition of methane at 3.39 mum.

Pulsed squeezed light: Simultaneous squeezing of multiple modes

We analyze the spectral properties of squeezed light produced by means of pulsed, single-pass degenerate parametric down-conversion. The multimode output of this process can be decomposed into characteristic modes undergoing independent squeezing evolution akin to the Schmidt decomposition of the biphoton spectrum. The main features of this decomposition can be understood using a simple analytical model developed in the perturbative regime. In the strong pumping regime, for which the perturbative approach is not valid, we present a numerical analysis, specializing to the case of one-dimensional propagation in a beta-barium borate waveguide. Characterization of the squeezing modes provides us with an insight necessary for optimizing homodyne detection of squeezing. For a weak parametric process, efficient squeezing is found in a broad range of local oscillator modes, whereas the intense generation regime places much more stringent conditions on the local oscillator. We point out that without meeting these conditions, the detected squeezing can actually diminish with the increasing pumping strength, and we expose physical reasons behind this inefficiency.

Synthesis and tomographic characterization of the displaced Fock state of light

Displaced Fock states of the electromagnetic field have been synthesized by overlapping the pulsed optical single-photon Fock state u1& with coherent states on a high-reflection beam splitter and completely characterized by means of quantum homodyne tomography. The reconstruction reveals nonclassical properties of displaced Fock states, such as negativity of the Wigner function and photon number oscillations. To our knowledge, this is the first time complete tomographic reconstruction has been performed on a highly nonclassical optical state.

Quantum-optical state engineering up to the two-photon level

Tailoring of arbitrary single-mode states of travelling light up to the two-photon level is proposed and demonstrated. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel.

Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements

A pulsed, balanced homodyne detector has been developed for precise measurement of the electric field quadratures of pulsed optical quantum states. A high level of common mode suppression (>85 dB) and low electronic noise (730 electrons per pulse) provide a signal-to-noise ratio of 14 dB for measurement of the quantum noise of individual pulses. Measurements at repetition rates as high as 1 MHz are possible. As a test, quantum tomography of the coherent state was performed, and the Wigner function and the density matrix were reconstructed with 99.5% fidelity. The detection system can be used for ultrarsensitive balanced detection in cw mode, e.g., for weak absorption measurements.