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Physical Review A

Photon subtraction and addition by a three-level atom in an optical cavity

Julio R. Gea-Banacloche, William Wilson

Published Sep 19, 2013• 17 citations
Publisher

Abstract

Rosenblum et al. showed recently that a three-level atom in a cavity can function as a perfect ``photon turnstile.'' Here we explore how this device reshapes the incident pulses, generalize it to the case of an input coherent state, and consider its use in reverse as a ``photon adder.'' We find that for initially unentangled pulses, adding one photon to an $|n\ensuremath{\rangle}$ number state is possible with a success probability equal to $1/(n+1)$.

DOI
10.1103/physreva.88.033832

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Rosenblum et al. showed recently that a three-level atom in a cavity can function as a perfect photon turnstile.'' Here we explore how this device reshapes the incident pulses, generalize it to the case of an input coherent state, and consider its use in reverse as a photon adder.'' We find that for initially unentangled pulses, adding one photon to an ∣n\ensuremath⟩|n\ensuremath{\rangle}∣n\ensuremath⟩ number state is possible with a success probability equal to 1/(n+1)1/(n+1)1/(n+1).
The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.
We study the interaction of a V-type atom in a cavity with incident single- and two-photon wavepackets and derive an exact formula, valid in all parameter regimes, relating the spectrum of the outgoing wavepackets to the incident one. We present detailed results for several special input pulses and consider the potential performance of the system as a CPHASE gate for initial pulses in a product state. We find values of the cavity, atomic, and pulse parameters that yield a conditional phase shift of π, albeit with a relatively small overlap between the incoming and outgoing pulse forms.
In atomic-scale or quantum physics, an electromagnetic field is composed of photons, optical packets so small that a typical laser pointer with 1mW of power emits billions of them each second. Being able to take away or add a single photon in a light field at will would be useful for accurate engineering of quantum states. Such pure single photons are ideal for carrying and manipulating information in emerging quantum technologies, but generating them still is very challenging. In quantum physics, subtraction or addition of a photon is not a deterministic process. Instead, the probability is proportional to the number of photons originally in the electromagnetic field. This is described by the equation â|n〉 = √ n|n − 1〉 and â†|n〉 = √ n+ 1|n + 1〉, where â and ↠are annihilation and creation operators, respectively, representing the action of subtracting and adding a photon in a field composed of n photons.1 Such single-photon operations were limited to pure theoretical discussions until 2004, when Grangier and coworkers found a simple way to subtract a photon2 from a field. Passing through a beam splitter of high transmittivity, some photons can be split from the initial field. A ‘click’ detected in the photodetector in the reflected channel means one photon has been subtracted from the field: see Figure 1(a). When the initial field is composed of a small number of photons, the effect is dramatic and may even completely change the characteristics of the field. For example, let us take an initial single-mode squeezed state generated by ‘degenerate’ parametric down-conversion, which is an optical nonlinear process that converts a pump photon into two twin photons with half the pump photon energy. (This state is well known for its quantum noise squeezed into one quadrature at the expense of expanded noise in the other quadrature.) In order to visualize the noise properties and characteristics of the squeezed state, a probability-like function, such Figure 1. Setups to subtract (a) and add (b) a single photon from/to a light field. ρin and ρout denote the density operators of the input and output fields; BS is a low-reflectivity beam splitter; PDC is a nonlinear crystal where parametric down-conversion takes place; â and ↠denote on/off photodetectors.
We consider the dynamics of single photons in a nonlinear optical cavity. When the Kerr nonlinearities of atomic dark resonances are utilized, the cavity mode is well described by a spin- 1/21/21/2 Hamiltonian. We show that it is possible to achieve coherent control of the cavity-mode wave function using $\ensuremath{\pi}$ pulses for single photons that switch the state of the cavity with very high accuracy. The underlying physics is best understood as the nonlinearity induced anticorrelation between single-photon injection/emission events, which we refer to as photon blockade. We also propose a method which uses these strong dispersive interactions to realize a single-photon turnstile device.
We have witnessed proliferate growth in theoretical and experimental efforts to understand and control physical systems in a quantum level. In a quantum optics laboratory, Gaussian states, whose phase properties are described by Gaussian probability-like functions, were generated but there was some limitation to use them for various tasks of quantum information processing. There have been suggestions and realisations to engineer the quantum state by subtracting or adding single photons from/to a Gaussian field. It is also possible to test fundamental quantum theories using these techniques. We discuss various issues in subtraction and addition of single photons.