We propose an efficient all-optical phase modulation based on a double-Λ system and demonstrate a π phase shift of a few-photon pulse induced by another few-photon pulse in cold rubidium atoms with this scheme. By changing the phases of the applied laser fields, one can control the property of the double-Λ medium. This phase-dependent mechanism makes the double-Λ system different form the conventional cross-Kerr-based system which only depends on the applied laser intensities. The proposed scheme provides a new route to generate strong nonlinear interactions between photons, and may have potential for applications in quantum information technologies.
We propose an efficient all-optical phase modulation based on a double-Λ system and demonstrate a π phase shift of a few-photon pulse induced by another few-photon pulse in cold rubidium atoms with this scheme. By changing the phases of the applied laser fields, one can control the property of the double-Λ medium. This phase-dependent mechanism makes the double-Λ system different form the conventional cross-Kerr-based system which only depends on the applied laser intensities. The proposed scheme provides a new route to generate strong nonlinear interactions between photons, and may have potential for applications in quantum information technologies.
We demonstrate an efficient cross-phase modulation (XPM) based on a closed-loop double-Λ system. The property of the double-Λ medium can be controlled by changing the phases of the applied optical fields. This phase-dependent XPM scheme can achieve large phase modulations at low-light intensities without requiring cavities or tightly focusing laser beams. With this scheme, we observe a π-level phase shift with two pulses, both consisting of eight photons in cold rubidium atoms. Such a novel scheme provides a simple route to generate strong interactions between photons and may have potential applications in all-optical quantum signal processing.
We theoretically investigate a double-Λ electromagnetically induced transparency (EIT) system. The property of the double-Λ medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-dependent mechanism differentiates the double-Λ medium from the conventional Kerr-based nonlinear medium, e.g., EIT-based nonlinear medium discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)], which depends only on the intensities of the applied laser fields. Steady-state analytical solutions for the phase-dependent system are obtained by solving the Maxwell-Bloch equations. In addition, we discuss efficient all-optical phase modulation and coherent light amplification based on the proposed double-Λ EIT scheme.
We investigate a four-level double-Lambda atomic scheme interacting with four laser fields, a weak probe field, a weak signal field and two driven fields, in a closed-loop configuration. We study the Kerr nonlinearity associated with cross-phase modulation based on electromagnetically induced transparency. Our results show, in this closed-loop system, that the strength of cross-phase modulation and two-photon absorption are dependent critically on the relative phase between the excitation paths. By choosing the parameters appropriately, large cross-phase modulation can be achieved within a wide transparency window, while two-photon absorption is cancelled completely. The strength of cross-phase modulation can be enhanced much more by decreasing the intensities of two driven fields.
We investigate a four-level double-Λ atomic scheme interacting with four laser fields, a weak probe field, a weak signal field and two driven fields, in a closed-loop configuration. We study the Kerr nonlinearity associated with cross-phase modulation based on electromagnetically induced transparency. Our results show, in this closed-loop system, that the strength of cross-phase modulation and two-photon absorption are dependent critically on the relative phase between the excitation paths. By choosing the parameters appropriately, large cross-phase modulation can be achieved within a wide transparency window, while two-photon absorption is cancelled completely. The strength of cross-phase modulation can be enhanced much more by decreasing the intensities of two driven fields.
Conditional- π phase shift between two photons is essential for entanglement generation and universal quantum logic. For photons, however, direct conditional controls are not possible and must be mediated by nonlinear media. Achieving such operations for photonic polarization qubits has remained difficult due to intrinsically weak photon-photon nonlinearities in atomic systems. Here, we show that a conditional- π phase shift between two weak coherent pulses can be realized via a cavityless closed double- Λ atomic system, where quantum interference between linear and nonlinear atom-photon interactions enables conditional control. By optimizing the interaction parameters, including amplitude and phase compensations, we identify the conditions for conditional- π phase shift between two weak coherent pulses. Experimentally, we observe the conditional- π phase shift with relative output amplitude 0.74 ± 0.06 and phase shift ( 0.95 ± 0.03 ) π between the two-photon amplitudes | H H 〉 and | V V 〉 . A theoretical analysis of Bell-state generation from weak coherent pulses further shows Clauser-Horne-Shimony-Holt inequality violation and nonzero concurrence. Our results clarify both the theoretical requirements and the experimental feasibility of cavityless atom-mediated nonlinearities for photonic quantum logic, establishing a scalable route toward nonlinear quantum photonics.
We present a theory of a continuous-wave light propagation in a medium of atoms with a double-$\ensuremath{\Lambda}$ configuration of levels. This is a configuration with a closed cycle of radiation-induced transitions. An interference of excitation channels in such closed-loop systems leads to a strong dependence of the atomic state on the relative phase and the relative amplitudes of applied electromagnetic waves. Therefore, the medium response may be controlled by the phases. On the other hand, the phases themselves change during the propagation. Thus the state of the medium and all the field parameters are tightly coupled to each other in the present problem. We consider the propagation of four-frequency laser radiation through the double-$\ensuremath{\Lambda}$ medium for two situations. At resonant or near-resonant excitation of atoms, both the medium and the field evolve into a nonabsorbing state. This state implies specific coherent superposition for atoms (``dark state''), and particular relations for the field phases, amplitudes, and frequencies. In this way, the propagation results in the phase, amplitude, and frequency matching of the laser waves. In the second case, one $\ensuremath{\Lambda}$ system in double-$\ensuremath{\Lambda}$ atoms is excited resonantly, while the second $\ensuremath{\Lambda}$ system is far off resonance. Such an excitation scheme ensures the preparation of atoms in the nearly dark state throughout the medium. Therefore, the total light energy is dissipated very weakly, whereas each individual laser wave can vary considerably along the propagation path. We have found that the resonant fields change as much as the far-detuned ones. The intensities oscillate sinusoidally with the optical length, with the energy being transferred back and forth between two waves in each frequency pair, resonant and far detuned. This gives the possibility for an almost lossless amplification of two of the laser waves, or an even generation of one of them.