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Physical Review Letters

Generation of Fock states of the electromagnetic field in a high-Qcavity through the Anderson localization

J. R. Kukliński

Published May 21, 1990• 18 citations
Publisher

Abstract

We investigate a high-Q cavity partially filled by a medium with ${\mathrm{\ensuremath{\chi}}}^{3}$ nonlinear susceptibility with a coherent signal having the form of a series of short pulses injected into it. We show that the electromagnetic field which builds up in the cavity has strong nonclassical features. For appropriate parameters Anderson localization occurs leading to the generation of states with a narrow photon-number probability distribution. We demonstrate that by adiabatic changing of the size of the cavity one may generate from the vacuum a nearly perfect Fock state of a chosen mode.

DOI
10.1103/physrevlett.64.2507

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We investigate a high-Q cavity partially filled by a medium with \ensuremathχ3{\mathrm{\ensuremath{\chi}}}^{3}\ensuremathχ3 nonlinear susceptibility with a coherent signal having the form of a series of short pulses injected into it. We show that the electromagnetic field which builds up in the cavity has strong nonclassical features. For appropriate parameters Anderson localization occurs leading to the generation of states with a narrow photon-number probability distribution. We demonstrate that by adiabatic changing of the size of the cavity one may generate from the vacuum a nearly perfect Fock state of a chosen mode.
We discuss a model of a cavity filled with a passive nonlinear ‚Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q − 1)th nonlinearity X (2q−1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X (3) nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.
We propose a scheme for quantum-light generation in a nonlinear cavity hybridized with a two-level system and theoretically show that, when excited by a series of controlled pump pulses, the hybrid source generates Fock states with high probabilities, e.g., one- and two-photon states can be generated near on demand, and Fock states with up to seven photons with a probability above 50%. The tailorable nature of the nonlinear cavity allows for generating Fock states with arbitrary frequencies, even with a fixed two-level system, creating fundamentally new opportunities in all areas of quantum technologies.
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.
We propose a scheme for the generation of various nonclassical states for a cavity field with a driven atom. In the scheme the atom is sent through the cavity and driven by a classical field. The atom interacts dispersively with the cavity field, which induces photon-number dependent Stark shift. Only for a desired Fock state, the atomic transition is tuned in resonance with the classical field. Thus, the measurement of the atomic transition may directly collapse the cavity field onto the desired Fock state. For a two-mode cavity field, pair coherent states and SU(2) coherent states can be generated.