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arXiv:1212.5486 · Physical Review Letters

P T Symmetry with a System of Three-Level Atoms

Chao Hang, Guoxiang Huang, V. V. Konotop

Published Feb 21, 2013• 276 citations
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Abstract

We show that a vapor of multilevel atoms driven by far-off-resonant laser beams, with the possibility of interference of two Raman resonances, is highly efficient for creating parity-time symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is antisymmetric in space. The spatial modulation of the probe-field susceptibility is achieved by a proper combination of standing-wave strong control fields and of Stark shifts induced by far-off-resonance laser fields. As particular examples we explore a mixture of isotopes of rubidium atoms and design a parity-time symmetric lattice and a parabolic refractive index with a linear imaginary part.

DOI
10.1103/physrevlett.110.083604

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We show that a vapor of multilevel atoms driven by far-off-resonant laser beams, with the possibility of interference of two Raman resonances, is highly efficient for creating parity-time symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is antisymmetric in space. The spatial modulation of the probe-field susceptibility is achieved by a proper combination of standing-wave strong control fields and of Stark shifts induced by far-off-resonance laser fields. As particular examples we explore a mixture of isotopes of rubidium atoms and design a parity-time symmetric lattice and a parabolic refractive index with a linear imaginary part.
In optical parity-time symmetry, the electric permittivity of an electromagnetic structure should have a real part, which is an even function of spatial coordinates, and an imaginary part, which is an odd function of coordinates. Since a Vee- and a Lambda-configuration three-level atomic vapor can be driven by both control and probe beams, and can exhibit both frequency-sensitive and field-controlling optical responses, the dielectric “constants” of these two atomic vapors can be tuned by manipulating the applied external control fields. The requirement for realizing optical parity-time symmetry can be fulfilled in quantum-coherent multilevel atomic vapors. A design based on Vee- and Lambda-configuration three-level atomic vapors for achieving optical parity-time symmetric interface is suggested in this paper. Under certain parameter conditions, an optical parity-time symmetric interface can possibly be fabricated in the present scenario of quantum-coherent multilevel atomic vapors.
PT\cal{PT}PT -symmetry in Rydberg atoms
We propose a scheme to realize parity-time ( PT )-symmetry in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. We show that Rydberg-dressed 87 Rb atoms in a four-level inverted Y -type configuration is highly efficient to generate the refractive index for a probe field, with a symmetric (antisymmetric) profile spatially in the corresponding real (imaginary) part. Comparing with earlier investigations, the present scheme provides a versatile platform to control the system from PT -symmetry to non- PT -symmetry via different external parameters, i.e. , coupling field detuning, probe field intensity and control field intensity.
We propose a realistic physical scheme to produce one-dimensional and two-dimensional weak-light solitons in an atomic system with PT\mathcal{PT}PT symmetry. The system we suggest is a cold three-level atomic gas with two species and is driven by control and probe laser fields. We show that by the interference of two Raman resonances a highly adjustable probe-field refractive index with PT\mathcal{PT}PT symmetry in one and two dimensions can be realized. We further show that it is possible to produce various light solitons when the weak nonlinearity of the probe field is taken into account. Due to the resonant character of the system, the light solitons obtained in one and two dimensions have extremely low light power (at the level of nanowatts). In addition, we demonstrate that the stability of these light solitons can be actively controlled via PT\mathcal{PT}PT phase transition of the system.
We present a physical setup for realizing all-real-spectrum optical potentials with arbitrary gain-and-loss distributions in a coherent medium consisting of a cold three-level atomic gas driven by control and probe laser fields. We show that by the interference of Raman resonances and the Stark shift induced by a far-detuned laser field, tunable, non-parity-time (non-PT)\mathcal{PT})PT)-symmetric optical potentials with all-real spectra proposed recently by Nixon and Yang [Phys. Rev. A 93, 031802(R) (2016)] can be actualized physically. We also show that when the real parts of the non-PT\mathcal{PT}PT-symmetric optical potentials are tuned cross certain thresholds, phase transitions---where the eigenspectrum of the system changes from all real to complex---may occur and hence the stability of the probe-field propagation is altered. Our scheme can also be extended to high dimensions and to a nonlinear propagation regime, where stable optical solitons with power of the order of nano-Watts may be generated in the system.
Enhancement and control of the index of refraction in a mixture of two three-level atomic species that form a pair of far-detuned $\ensuremath{\Lambda}$ schemes under two-photon resonance has been studied. We employ the density-matrix approach to properly take population relaxation into account and to describe the interaction of each $\ensuremath{\Lambda}$ system with the electromagnetic fields. Both $\ensuremath{\Lambda}$ systems are driven by a corresponding far-detuned coherent field at one atomic transition and are probed by the same weak field. In the dressed-state basis, it represents a superposition of effective two-level subsystems with the positions, widths, and amplitudes of the resonances controlled by the driving fields and allows for efficient control of the susceptibility of the total system; leading to refractive index (RI) enhancement with vanishing absorption in the absence of amplification. We analyze the experimental implementation of such a system in a cell of Rb atoms with a natural abundance of isotopes. An upper limit estimate of the RI enhancement is obtained.