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arXiv:quant-ph/0312135 · Physical Review Letters

Homodyne Tomography Characterization and Nonlocality of a Dual-Mode Optical Qubit

С. А. Бабичев, J. Appel, Alexander I. Lvovsky

Published May 14, 2004• 118 citations
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Abstract

A single photon, delocalized over two optical modes, is characterized by means of quantum homodyne tomography. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical quantum bit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments.

DOI
10.1103/physrevlett.92.193601

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A single photon, delocalized over two optical modes, is characterized by means of quantum homodyne tomography. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical quantum bit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments.
We present experimental homodyne tomography of an optical quantum bit represented by a single photon split into two optical modes. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical qubit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments. We also show that a homodyne measurement on just one of the modes leads to remote preparation of a single-rail optical qubit in the other mode.
We have developed a technique for dual-temporal-mode, ultrafast, time-domain, balanced homodyne detection. We have tested it by performing homodyne measurements on pairs of picosecond-duration temporal modes (or “time bins”) carrying a delocalized single photon. The experimental homodyne data have been used to reconstruct both the density matrix and the two-mode Wigner function of the delocalized state, thus showing the correlations existing between the pair of temporal modes carrying the single photon.
Precise information about the temporal mode of optical states is crucial for optimizing their interaction efficiency between themselves and/or with matter in various quantum communication devices. Here we propose and experimentally demonstrate a method of determining both the real and imaginary components of a single photon's temporal density matrix by measuring the autocorrelation function of the photocurrent from a balanced homodyne detector at multiple local oscillator frequencies. We test our method on single photons heralded from biphotons generated via four-wave mixing in an atomic vapor and obtain excellent agreement with theoretical predictions for several settings. A convenient scheme for characterizing the temporal properties of a single photon looks set to aid experiments in quantum optics. An international team of scientists from Canada, China, USA, Uruguay and Russia says that this approach can be used to determine the complete mode structure of a photon, in particular, the real and imaginary parts of its temporal density matrix. This information is important for quantum communication experiments for which it is often critical to match photon modes. The characterization scheme, which the researchers term polychromatic optical heterodyne tomography, works by collecting autocorrelation data of homodyne photocurrent at multiple local oscillator frequencies. The team says that tests of the technique with single photons generated by four-wave mixing in an atomic vapour agree well with theoretical predictions.
We present a review of our recent studies concerning remotely prepared entangled bits (ebits) made of a single photon coherently delocalized between two well-separated temporal modes (or time bins). The preparation scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is analyzed by performing both single-mode and two-mode homodyne tomography with the ultra-fast balanced homodyne detection scheme recently developed in our lab. Beside the non-classical behavior typical of single-photon Fock states (negative values around the origin), the reconstructed two-mode Wigner function is found to be characterized by an intriguing phase and by correlations between the two distant time bins sharing the single photon.
e present a review of our recent studies concerning remotely prepared entangled bits (ebits) made of a single photon coherently delocalized between two well-separated temporal modes (or time bins). The preparation scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is analyzed by performing both single-mode and two-mode homodyne tomography with the ultra-fast balanced homodyne detection scheme recently developed in our lab. Beside the non-classical behavior typical of single-photon Fock states (negative values around the origin), the reconstructed two-mode Wigner function is found to be characterized by an intriguing phase and by correlations between the two distant time bins sharing the single photon.