There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

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Gaussian quantum information

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

/pdf/gaussian-quantum-information-3johze75r1.pdf

Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

Parametric downconversion (PDC) in waveguides offers compact setups and high design flexibility in terms of the temporal-spectral properties of the generated photon pairs. It is thus a versatile source for a large number of quantum states with applications in quantum communication or quantum networks. One key element of those systems is the interference of quantum states from different, independent sources at e.g. beamsplitters with high visibility. Those sources should therefore not only meet demands of brightness and efficiency but also generate pure photons with identical properties, in particular in the frequency degree of freedom. In the context of PDC, such states are called decorrelated as there are no spatio-temporal correlations between signal and idler. They can be realized in bulk materials and waveguides by tailoring the pump and dispersion properties. The first source of this kind was demonstrated in bulk KDP at near-infrared wavelengths. For telecom wavelengths a bright, decorrelated source in a waveguide structure was realized in periodically poled KTP. However, in these sources the spectral properties of the signal and idler photons are still dissimilar.

Decorrelated PDC source at telecom wavelengths with identical signal and idler

We describe a novel phenomenon occurring when a polarized Gaussian beam of light is observed in a Cartesian reference frame whose axes are not parallel to the direction of propagation of the beam Such phenomenon amounts to an intriguing spin-dependent shift of the position of the center of the beam, with manners akin to the spin Hall effect of light We demonstrate that this effect is unavoidable when the light beam possesses a nonzero transverse angular momentum

Geometric Spin Hall Effect of Light

We present advances in the use of gigahertz LiNbO3 modulators enabling us programmable delays, which we will use to implement a multiplexed single-photon source, based on birefringent phase-matching in KTP waveguides.

Time-Frequency Multiplexed Single-Photon Source Based on LiNbO 3 Modulators

We report on a novel phase-locking technique for fiber-based Mach-Zehnder interferometers based on discrete single-photon detections, and demonstrate this in a setup. Our interferometer decodes relative-phase-encoded optical pulse pairs for quantum key distribution applications and requires no locking laser in addition to the weak received signal. Our new simple locking scheme is shown to produce an Ornstein-Uhlenbeck dynamic and achieve optimal phase noise for a given count rate. In case of wavelength drifts that arise during the reception of Doppler-shifted satellite signals, the arm-length difference gets continuously readjusted to keep the interferometer phase stable.

Phase-locking an interferometer with single-photon detections

We present results on nonlinear electro-optical conversion of microwave radiation into the optical telecommunication band with more than 0.1% photon number conversion efficiency with MHz bandwidth, in a crystalline whispering gallery mode resonator.

Christoph Marquardt

Papers

Decorrelated PDC source at telecom wavelengths with identical signal and idler

Geometric Spin Hall Effect of Light

Time-Frequency Multiplexed Single-Photon Source Based on LiNbO 3 Modulators

Phase-locking an interferometer with single-photon detections

Single sideband microwave to optical photon conversion – an electro-optic realization