Deterministic generation of tailored-optical-coherent-state superpositions

Abstract

Pulsed coherent excitation of a two-level atom strongly coupled to a resonant cavity mode will create a superposition of two coherent states of opposite amplitudes in the field. By choosing proper parameters of interaction time and pulse shape the field after the pulse will be almost disentangled from the atom and can be efficiently outcoupled through cavity decay. The fidelity of the generation approaches unity if the atom-field coupling strength is much larger than the atomic and cavity decay rates. This implies a strong difference between even and odd output photon number counts. Alternatively, the coherence of the two generated field components can be proven by phase-dependent annihilation of the generated nonclassical superposition state by a second pulse. . Recently, it has been noted that such states could also be used in quantum-information processing for encoding qubits in the relative phase of the two classical amplitude [3]. In principle they allow quantum teleportation and linear quantum gates in a straightforward manner [4]. Although nondeterministic sources could be used for these applications it would clearly be more desirable if a controlled deterministic source was available in the optical domain.Nonlinear optical setups, such as, e.g., a subthreshold optical parametric oscillator or electrically induced transparency type interactions in atomic media, have been suggested as possible sources of such states [5]. Alternatively, traveling-wave coherent-superposition states might be generated by sending a three-level atom in a superposition state of the two lower levels through a high-Q cavity, which couples only one of the levels with a third upper state [6]. The desired quantum state is then generated by sending a light pulse through the cavity followed by postselection on the outcome of a subsequent proper projective measurement on the atom. In this way, the microscopic quantum superposition of the atom is transformed to a macroscopic superposition of the light field being transmitted or reflected from the cavity. Although this scheme works well in principle it is slow and hard to implement in practice.Here we propose a significantly simpler version of a cavity QED scheme using just a two-level atom resonantly coupled to a single mode of a high-Q cavity mode with a coupling strength g exceeding the natural linewidth ␥ of the atomic transition and the cavity decay rate (Fig. 1). All that is needed is to apply a coherent driving pulse of proper strength and duration to the atom from the side. The induced Rabi flopping of the atom together with coherent scattering of the pulse light into the cavity mode then generate the desired field state. Interestingly, it is possible to tailor the interaction time in such a way that the atom gets disentangled from the field after the pulse so that no projective measurement on the atom is required. This is a central difference from previous suggestions of using a far-detuned pulse. Such a pulse creates a similar field, but as it induces no atomic transitions it le...

Quantum-enhanced interferometry with cavity QED-generated non-classical light

“…Clearly, it is crucial to extract enough photons out of the mode to create a propagating non-classical wavepacket. For cat states (achieved in the ideal preparation scheme), a single photon lost from the wave-packet renders the output state classical [30]. However, as we will show next, the SNL can still be beaten in presence of an imperfect extraction once we are dealing with more classical states, as those obtained after the imperfect preparation scheme discussed above.…”

“…The need to extract photons from the cavity directly reveals the twofold role of the photon leakage. On the one hand, during the state preparation photon leakage is detrimental to the atom-field entanglement as it provides potential information on the state of the system [53] and therefore limits the interferometric precision. At first sight this suggests fast state preparation during which photons are not detected outside the cavity.…”

“…Similar proposals followed in the optical regime [29][30][31]33,34] where the generated field emitted from the resonator can be directly analyzed or used for interferometric protocols, as studied in the following. Recent technical progress in microwave amplification and detection also allows for direct microwave photon detection in the co-planar waveguide cavities [35].…”

“…Here we discuss a quantum non-demolition (QND) protocol [28][29][30][31] involving an optical cavity mode interacting with a single atom. We demonstrate that this protocol yields a non-classical state of light [32] that combined with a coherent pulse at the input of an optical interferometer can provide SSN sensitivity of the phase estimation.…”

Schrödinger Cat States for Quantum Information Processing

“…Some success has been reported in creating such superposition states within high Q cavities in the microwave [7] and optical [35] domains. Simplified versions of cavity QED schemes have been developed for deterministic generation of cat states in a cavity [47]. While this method is relatively effective to generate cat states in cavity, most of the schemes suggested for quantum information processing with coherent states require free propagating cat states.…”