Control over the internal states of trapped ions makes them the ideal system to generate single and two-photon states. Coupling a single ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape, phase and frequency. Using the long coherence time of the ion's internal states and employing a scheme to protect the coherence of the ion-cavity interaction, we demonstrate the generation of a two-photon entangled state with full control over the phase. Initially, ion-photon entanglement is generated. A second photon is subsequently generated, mapping the ion's state onto the second photon. By adjusting the drive field the phase of the entangled state can be fully controlled. We implement this scheme in the most resource efficient way by utilizing a single $^{40}$ Ca $^+$ ion coupled to an optical cavity and demonstrate the generation of a two-photon entangled stated with full phase control with a fidelity of up to 82\%.Control over the internal states of trapped ions makes them the ideal system to generate single and two-photon states. Coupling a single ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape, phase and frequency. Using the long coherence time of the ion's internal states and employing a scheme to protect the coherence of the ion-cavity interaction, we demonstrate the generation of a two-photon entangled state with full control over the phase. Initially, ion-photon entanglement is generated. A second photon is subsequently generated, mapping the ion's state onto the second photon. By adjusting the drive field the phase of the entangled state can be fully controlled. We implement this scheme in the most resource efficient way by utilizing a single $^{40}$Ca$^+$ ion coupled to an optical cavity and demonstrate the generation of a two-photon entangled stated with full phase control with a fidelity of up to 82\%.

quant-pharXiv:2601.16875Physical Review LettersJan 26, 20260 citations

Beyond the Random Phase Approximation

J. D. Fan, Y. M. Malozovsky

Quantum MatterJul 2, 20151 citation

Generation of number-phase minimum-uncertainty states and number states

Y. Yamamoto, S. Machida, N. Imoto +2 more

The difference between the two nonclassical photon states, i.e., the squeezed state and the number-phase minimum-uncertainty state, is discussed. Four different generation principles for number-phase minimum-uncertainty states (and number states) are described. They are the following: (1) unitary evolution, using self-phase modulation and interference; (2) nonunitary state reduction, using either quantum nondemolition photon-number measurement or parametrically amplified idler-wave photon counting; (3) negative-feedback oscillators, incorporating a correlated photon-pair generator; and (4) pump-amplitude noise-suppressed lasers. A number-phase minimum-uncertainty state with photon-number noise reduced to 1 dB (20%) below the standard quantum limit in a frequency range over 100 MHz was produced by the fourth-generation principle.The difference between the two nonclassical photon states, i.e., the squeezed state and the number-phase minimum-uncertainty state, is discussed. Four different generation principles for number-phase minimum-uncertainty states (and number states) are described. They are the following: (1) unitary evolution, using self-phase modulation and interference; (2) nonunitary state reduction, using either quantum nondemolition photon-number measurement or parametrically amplified idler-wave photon counting; (3) negative-feedback oscillators, incorporating a correlated photon-pair generator; and (4) pump-amplitude noise-suppressed lasers. A number-phase minimum-uncertainty state with photon-number noise reduced to 1 dB (20%) below the standard quantum limit in a frequency range over 100 MHz was produced by the fourth-generation principle.

Journal of the Optical Society of America BOct 1, 198770 citations

Phase Geometry

S. Werner

Jan 1, 20250 citations

Getting coherent state superpositions to stay put in phase space: $Q$ functions and one dimensional integral representations of generator eigenstatesGetting coherent state superpositions to stay put in phase space: $Q$ functions and one dimensional integral representations of generator eigenstates

Mayukh Nilay Khan

We study quantum mechanics in the phase space associated with the coherent state (CS) manifold of Lie groups. Eigenstates of generators of the group are constructed as one dimensional integral superpositions of CS along their orbits. We distinguish certain privileged orbits where the superposition is in phase. Interestingly, for closed in phase orbits, the geometric phase must be quantized to $2π\mathbb{Z}$ , else the superposition vanishes. This corresponds to exact Bohr-Sommerfeld quantization. The maximum of the Husimi-Kano $Q$ quasiprobability distribution is used to diagnose where in phase space the eigenstates of the generators lie. The $Q$ function of a generator eigenstate is constant along each orbit. We conjecture that the maximum of the $Q$ function corresponds to these privileged in phase orbits. We provide some intuition for this proposition using interference in phase space, and then demonstrate it for canonical CS ( $H_4$ oscillator group), spin CS ( $SU(2)$ ) and $SU(1,1)$ CS, relevant to squeezing.We study quantum mechanics in the phase space associated with the coherent state (CS) manifold of Lie groups. Eigenstates of generators of the group are constructed as one dimensional integral superpositions of CS along their orbits. We distinguish certain privileged orbits where the superposition is in phase. Interestingly, for closed in phase orbits, the geometric phase must be quantized to $2π\mathbb{Z}$, else the superposition vanishes. This corresponds to exact Bohr-Sommerfeld quantization. The maximum of the Husimi-Kano $Q$ quasiprobability distribution is used to diagnose where in phase space the eigenstates of the generators lie. The $Q$ function of a generator eigenstate is constant along each orbit. We conjecture that the maximum of the $Q$ function corresponds to these privileged in phase orbits. We provide some intuition for this proposition using interference in phase space, and then demonstrate it for canonical CS ($H_4$ oscillator group), spin CS ($SU(2)$) and $SU(1,1)$ CS, relevant to squeezing.

arXiv:1911.09966Nov 22, 20190 citations

^{40}

^+

ion coupled to an optical cavity and demonstrate the generation of a two-photon entangled stated with full phase control with a fidelity of up to 82\%.

Getting coherent state superpositions to stay put in phase space:

Q

functions and one dimensional integral representations of generator eigenstates

2π\mathbb{Z}

, else the superposition vanishes. This corresponds to exact Bohr-Sommerfeld quantization. The maximum of the Husimi-Kano

Q

quasiprobability distribution is used to diagnose where in phase space the eigenstates of the generators lie. The

Q

function of a generator eigenstate is constant along each orbit. We conjecture that the maximum of the

Q

function corresponds to these privileged in phase orbits. We provide some intuition for this proposition using interference in phase space, and then demonstrate it for canonical CS (

H_4

oscillator group), spin CS (

SU(2)

) and

SU(1,1)

CS, relevant to squeezing.