Parametric Oscillation with Squeezed Vacuum Reservoirs

Employing the quantum Hamiltonian describing the interaction of two-mode light (signal-idler modes) generated by a nondegenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master equation. The corresponding Fokker-Planck equation for the Q-function is then solved employing a propagator method developed in Ref. \cite{1}. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal-idler modes are in squeezed states and the squeezing occurs in the first quadrature. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in the first quadrature can be achieved.Comment: 16 page

Squeezing spectra from s-ordered quasiprobability distributions. Application to dispersive optical bistability

It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s-ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s-ordered quasiprobability distribution verifies a true Fokker-Planck equation, i.e., the Langevin equations used for deriving the squeezing spectrum are not exact. The (linearized) intracavity squeezing obtained from any s-ordered distribution is also exact. These results are exemplified in the problem of dispersive optical bistability.Comment: 15 pages, no figures, to be published in Journal of Modern Optic

Realization of GHZ States and the GHZ Test via Cavity QED

In this article we discuss the realization of atomic GHZ states involving three-level atoms and we show explicitly how to use this state to perform the GHZ test in which it is possible to decide between local realism theories and quantum mechanics. The experimental realizations proposed makes use of the interaction of Rydberg atoms with a cavity prepared in a coherent state.Comment: 16 pages and 3 figures. submitted to J. Mod. Op

Quadrature squeezed photons from a two-level system.

Resonance fluorescence arises from the interaction of an optical field with a two-level system, and has played a fundamental role in the development of quantum optics and its applications. Despite its conceptual simplicity, it entails a wide range of intriguing phenomena, such as the Mollow-triplet emission spectrum, photon antibunching and coherent photon emission. One fundamental aspect of resonance fluorescence--squeezing in the form of reduced quantum fluctuations in the single photon stream from an atom in free space--was predicted more than 30 years ago. However, the requirement to operate in the weak excitation regime, together with the combination of modest oscillator strength of atoms and low collection efficiencies, has continued to necessitate stringent experimental conditions for the observation of squeezing with atoms. Attempts to circumvent these issues had to sacrifice antibunching, owing to either stimulated forward scattering from atomic ensembles or multi-photon transitions inside optical cavities. Here, we use an artificial atom with a large optical dipole enabling 100-fold improvement of the photon detection rate over the natural atom counterpart and reach the necessary conditions for the observation of quadrature squeezing in single resonance-fluorescence photons. By implementing phase-dependent homodyne intensity-correlation detection, we demonstrate that the electric field quadrature variance of resonance fluorescence is three per cent below the fundamental limit set by vacuum fluctuations, while the photon statistics remain antibunched. The presence of squeezing and antibunching simultaneously is a fully non-classical outcome of the wave-particle duality of photons.We acknowledge financial support from the University of Cambridge, the European Research Council ERC Consolidator Grant Agreement No. 617985 and the EU-FP7 Marie Curie Initial Training Network S3NANO. C.M. acknowledges Clare College Cambridge for financial support through a Junior Research Fellowship.This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nature1486

A generalization of the Entropy Power Inequality to Bosonic Quantum Systems

In most communication schemes information is transmitted via travelling modes of electromagnetic radiation. These modes are unavoidably subject to environmental noise along any physical transmission medium and the quality of the communication channel strongly depends on the minimum noise achievable at the output. For classical signals such noise can be rigorously quantified in terms of the associated Shannon entropy and it is subject to a fundamental lower bound called entropy power inequality. Electromagnetic fields are however quantum mechanical systems and then, especially in low intensity signals, the quantum nature of the information carrier cannot be neglected and many important results derived within classical information theory require non-trivial extensions to the quantum regime. Here we prove one possible generalization of the Entropy Power Inequality to quantum bosonic systems. The impact of this inequality in quantum information theory is potentially large and some relevant implications are considered in this work

Non-Gaussian states for continuous variable quantum computation via Gaussian maps

We investigate non-Gaussian states of light as ancillary inputs for generating nonlinear transformations required for quantum computing with continuous variables. We consider a recent proposal for preparing a cubic phase state, find the exact form of the prepared state and perform a detailed comparison to the ideal cubic phase state. We thereby identify the main challenges to preparing an ideal cubic phase state and describe the gates implemented with the non-ideal prepared state. We also find the general form of operations that can be implemented with ancilla Fock states, together with Gaussian input states, linear optics and squeezing transformations, and homodyne detection with feed forward, and discuss the feasibility of continuous variable quantum computing using ancilla Fock states.Comment: 8 pages, 6 figure

A semiconductor source of triggered entangled photon pairs?

The realisation of a triggered entangled photon source will be of great importance in quantum information, including for quantum key distribution and quantum computation. We show here that: 1) the source reported in ``A semiconductor source of triggered entangled photon pairs''[1. Stevenson et al., Nature 439, 179 (2006)]} is not entangled; 2) the entanglement indicators used in Ref. 1 are inappropriate, relying on assumptions invalidated by their own data; and 3) even after simulating subtraction of the significant quantity of background noise, their source has insignificant entanglement.Comment: 5 pages in pre-print format, 1 tabl

Observation of squeezed light from one atom excited with two photons

Single quantum emitters like atoms are well-known as non-classical light sources which can produce photons one by one at given times, with reduced intensity noise. However, the light field emitted by a single atom can exhibit much richer dynamics. A prominent example is the predicted ability for a single atom to produce quadrature-squeezed light, with sub-shot-noise amplitude or phase fluctuations. It has long been foreseen, though, that such squeezing would be "at least an order of magnitude more difficult" to observe than the emission of single photons. Squeezed beams have been generated using macroscopic and mesoscopic media down to a few tens of atoms, but despite experimental efforts, single-atom squeezing has so far escaped observation. Here we generate squeezed light with a single atom in a high-finesse optical resonator. The strong coupling of the atom to the cavity field induces a genuine quantum mechanical nonlinearity, several orders of magnitude larger than for usual macroscopic media. This produces observable quadrature squeezing with an excitation beam containing on average only two photons per system lifetime. In sharp contrast to the emission of single photons, the squeezed light stems from the quantum coherence of photon pairs emitted from the system. The ability of a single atom to induce strong coherent interactions between propagating photons opens up new perspectives for photonic quantum logic with single emittersComment: Main paper (4 pages, 3 figures) + Supplementary information (5 pages, 2 figures). Revised versio

Scheme for generating entangled states of two field modes in a cavity

This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes-Cummings model. For some particular field states, coherent and squeezed states, the transformation between the two bare basis's, related by the unitary transformation, becomes particularly simple. It is shown how to generate, the highly non-classical, entangled coherent states of the two modes, both in the zero and large detuning cases. An advantage with the zero detuning case is that the preparation is deterministic and no atomic measurement is needed. For the large detuning situation a measurement is required, leaving the field in either of two orthogonal entangled coherent states.Comment: Accepted in J. Mod. Opt.; 12 pages; Replaced with revised version. Extended discussion of experimental realizations, earlier studies in the field and on the frequency dependence in the adiabatic eliminatio

Resolving photon number states in a superconducting circuit

Electromagnetic signals are always composed of photons, though in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting qubit to signals on a microwave transmission line, it is possible to construct an integrated circuit where the presence or absence of even a single photon can have a dramatic effect. This system is called circuit quantum electrodynamics (QED) because it is the circuit equivalent of the atom-photon interaction in cavity QED. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit can absorb and re-emit a single photon many times. Here, we report a circuit QED experiment which achieves the strong dispersive limit, a new regime of cavity QED in which a single photon has a large effect on the qubit or atom without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability to find the corresponding photon number in the cavity. This effect has been used to distinguish between coherent and thermal fields and could be used to create a photon statistics analyzer. Since no photons are absorbed by this process, one should be able to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.Comment: 6 pages, 4 figures, hi-res version at http://www.eng.yale.edu/rslab/papers/numbersplitting_hires.pd