We propose and analyze an efficient scheme for the lopsided Raman-Nath diffraction of one-dimensional (
1D) and two-dimensional (
2D) atomic gratings with periodic parity-time (
PT)-symmetric refractive index. The atomic grating is constructed by the cold-atomic vapor with two isotopes of rubidium, which is driven by weak probe field and space-dependent control field. Using experimentally achievable parameters, we identify the conditions under which
PT-symmetric refractive index allows us to observe the lopsided Raman-Nath diffraction phenomenon and improve the diffraction efficiencies beyond what is achievable in a conventional atomic grating. The nontrivial atomic grating is a superposition of an amplitude grating and a phase grating. It is found that the lopsided Raman-Nath diffraction at the exceptional point (EP) of
PT-symmetric grating originates from constructive and destructive interferences between the amplitude and phase gratings. Furthermore, we show that the
PT-phase transition from unbroken to broken
PT-symmetric regimes can modify the asymmetric distribution of the diffraction spectrum and that the diffraction efficiencies in the non-negative diffraction orders can be significantly enhanced when the atomic grating is pushed into a broken
PT-symmetric phase. In addition, we also analyze the influence of the grating thickness on the diffraction spectrum. Our scheme may provide the possibility to design a gain-beam splitter with tunable splitting ratio and other optical components in integrated optics.
Rb) atomic ensemble with a non-Hermitian optical structure, in which a lopsided optical diffraction grating can be realized just with the combination of single spatially periodic modulation and loop-phase. Parity-time (PT) symmetric and parity-time antisymmetric (APT) modulation can be switched by adjusting different relative phases of the applied beams. Both PT symmetry and PT antisymmetry in our system are robust to the amplitudes of coupling fields, which allows optical response to be modulated precisely without symmetry breaking. Our scheme shows some nontrivial optical properties, such as lopsided diffraction, single-order diffraction, asymmetric Dammam-like diffraction, etc. Our work will benefit the development of versatile non-Hermitian/asymmetric optical devices.
Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g., with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.
Abstract A scheme for two-dimensional (2D) electromagnetically induced grating via spatial gain and phase modulation is presented in a two-level atomic system. Based on the interactions of two orthogonal standing-wave fields, the atom could diffract the weak probe beam into high-order directions and a 2D diffraction grating is generated. It is shown that the diffraction efficiency of the grating can be efficiently manipulated by controlling the Rabi frequencies of control fields, the detunings of the control and probe fields, and interaction length. Different from 2D cross-grating via electromagnetically induced transparency in a four-level atomic system, the present scheme results from the spatial modulation of gain and phase in a simple two-level system, which could lead to 2D gain-phase grating with larger diffraction intensities in the diffraction directions. The studies we present may have potential applications in developing photon devices for optical-switching, optical imaging and quantum information processing.
Understanding and manipulating the non-Hermitian optical property based on coherent atomic gases is of great importance and has attracted much theoretical and experimental attentions. Advancing this study to the nonlinear optics regime is highly desirable due to its importance in fundamental physics and potential applications. In this work, we propose to realize a tunable electromagnetically induced grating (EIG) with parity-time (
PT) symmetry in a cold gas of Rydberg atoms, where interatomic interactions between Rydberg states are mapped to strong and long-range optical interactions, and investigate nonlinear light diffractions in this system. We show that for far-field diffraction, laser beams incident upon the
PT-symmetric EIG display distinctive asymmetric diffraction fringes, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms. For near-field diffraction, the nonlinear Talbot diffraction carpets emerge and can be modulated by
PT symmetry in the presence of strong nonlocal interactions, allowing the realization of controllable optical self-imaging. The results are not only imperative for the study of non-Hermitian nonlinear optics but also useful for characterizing the interatomic interaction in Rydberg gases and for designing new optical devices useful in optical information processing and transmission.
Lossy atomic photonic crystals can be suitably tailored so that the real and imaginary parts of the susceptibility are, respectively, an odd and an even function of position. Such a parity-time
(PT) space antisymmetry in the susceptibility requires neither optical gain nor negative refraction, but is rather attained by a combined control of the spatial modulation of both the atomic density and their dynamic level shift. These passive photonic crystals made of dressed atoms are characterized by a tunable unidirectional reflectionlessness accompanied by an appreciable degree of transmission. Interestingly, such peculiar properties are associated with non-Hermitian degeneracies of the crystal scattering matrix, which can then be directly observed through reflectivity measurements via a straightforward phase modulation of the atomic dynamic level shift and even off resonance.