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Journal of the Optical Society of America B

Optical Fock-state generation with large number of photons based on atoms coupled to an optical parametric oscillator

Jing Zhang, Junmin Wang, Tiancai Zhang

Published Jun 1, 2012• 5 citations
Publisher

Abstract

An optical field with a definite number of photons is very important for quantum metrology and quantum information. Some theoretical protocols for creating such a Fock-state have been proposed, but it is still a big challenge to produce it with a large number photons experimentally. We revisit the system of atoms inside an optical parametric oscillator that was proposed in 1990s, and it is found that for the atom ensemble, the optical Fock-state with an arbitrary number of photons can be generated. Compared to the previous proposals, the scheme presented here is simple and seems physically realizable. The system also provides the possibility to demonstrate the strong interaction between nonclassical light and atoms in a confined space.

DOI
10.1364/josab.29.001473

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An optical field with a definite number of photons is very important for quantum metrology and quantum information. Some theoretical protocols for creating such a Fock-state have been proposed, but it is still a big challenge to produce it with a large number photons experimentally. We revisit the system of atoms inside an optical parametric oscillator that was proposed in 1990s, and it is found that for the atom ensemble, the optical Fock-state with an arbitrary number of photons can be generated. Compared to the previous proposals, the scheme presented here is simple and seems physically realizable. The system also provides the possibility to demonstrate the strong interaction between nonclassical light and atoms in a confined space.
The preparation of Fock states, as a fundamental problem in the research of quantum optics and quantum information, still faces challenges in achieving both unconditional preparation and large photon numbers. Here, we study the deterministic generation of large Fock states through the nonlinear interaction in coupled optical-optomechanical cavities. Under the condition that the mechanical frequency is twice the optical coupling strength, and much larger than the optomechanical coupling strength, there occurs a nonlinear interaction among two optical eigenmodes and the mechanical mode, i.e., a photon is annihilated, accompanied by the creation of another photon together with a phonon, and vice versa. It is analytically proved that, through this interaction, Fock states | n 〉 and | 1 〉 will generate | n + 1 〉 at specific evolution times if the mechanical mode is initially on the ground state. In addition, numerical results show that Fock states | n 〉 and | p 〉 can also generate | n + p 〉 with the fidelities larger than 94% ( 1 < p ≤ n ≤ 40 ). The proposed mechanism achieves deterministic generation of large Fock states, which can be applied to quantum metrology and quantum simulation.
The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n -photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n ( n > 10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.
Fock states are quantized states of electromagnetic waves with diverse applications in quantum optics and quantum communication. However, the generation of arbitrary optical Fock states still remains elusive. Most Fock-state-generation proposals rely on precisely controlling the atom-cavity interactions and are experimentally challenging. We propose a scheme to distill an optical Fock state from a coherent state. A conditional phase flip with arbitrary phase is implemented between the atom and light. The conditional phase flip along with unitary rotations and measurements on the atoms enables us to distill the required Fock state. As an example, we show the distillation of Fock state ∣100⟩|100⟩∣100⟩.
I consider several interesting aspects of a new light source, a two-level atom, or N two-level atoms inside an optical parametric oscillator. I find that in the weak driving limit, detection of a transmitted or fluorescent photon generates a highly entangled state of the atom and the cavity. This entanglement can be used with beam splitters to create more complex quantum states and implement teleportation protocols. Also, one can store a single photon in the atoms, along the lines of recent slow and stopped light proposals and experiments.
We study the generation of strongly correlated photons by coupling an atom to photonic quantum fields in a one-dimensional waveguide. Specifically, we consider a three-level or four-level system for the atom. Photon-photon bound states emerge as a manifestation of the strong photon-photon correlation mediated by the atom. Effective repulsive or attractive interaction between photons can be produced, causing either suppressed multiphoton transmission (photon blockade) or enhanced multiphoton transmission (photon-induced tunneling). As a result, nonclassical light sources can be generated on demand by sending coherent states into the proposed system. We calculate the second-order correlation function of the transmitted field and observe bunching and antibunching caused by the bound states. Furthermore, we demonstrate that the proposed system can produce photon pairs with a high degree of spectral entanglement, which have a large capacity for carrying information and are important for large-alphabet quantum communication.