Optical PT-symmetry and PT-antisymmetry in coherently driven atomic lattices

Discrete dynamics of light in an anti-parity-time symmetric photonic lattice in atomic vapors

We demonstrate the realization of an anti-parity-time (PT)-symmetric photonic lattice in a coherent three-level Λ-type 85Rb atomic system both experimentally and theoretically. Such an instantaneously reconfigurable anti-PT-symmetric photonic lattice is "written" by two one-dimensional coupling fields, which are arranged alternately along the x direction and can modulate the refractive index of the atomic vapor in a spatially periodical manner via controllable atomic coherence. By properly adjusting the relevant atomic parameters, the phase shift between two adjacent lattice channels occurs in the constructed non-Hermitian photonic system. Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems.

Three-color reflections in one-dimensional ordered and disordered atomic lattices with trapped N-type cold atoms

Investigating and controlling light propagation in one-dimensional (1D) ordered and disordered atomic lattices is critical both fundamentally and for applications. In this study, cold atoms are trapped in 1D optical lattice and driven to the four-level N configuration. In each period, the atoms exhibit a Gaussian density distribution with the average atomic density N₀ (1 + Δ_k). When the random number Δ_k = 0 (the atomic density N_k(z)) corresponding to an ordered 1D atomic lattice, there are three reflection regions of high reflectivity located in two EIT windows and one large detuning range. However, the atomic density may increase (N k+(z) with Δ_k > 0) or decrease (N k-(z) with Δ_k < 0) owing to the imperfect manufacturing process or random distribution of atoms corresponding to a disordered atomic lattice. The results show that the width and height of reflections can be raised (reduced) by the increased (decreased) ratio of N k+(z)/N _k (z) (N k-(z)/N _k (z)) with the random distribution of lattice cells with N k+(z) (N k-(z)). When a cluster of disordered lattice cells with N k+(z) and N k-(z) is located at the front or tail of the atomic lattice, reflection symmetry can be broken. However, the symmetry and robustness can be well preserved with the random fluctuation of the average atomic density in each lattice cell.

Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices

Past decades have witnessed the emergence and increasing expansion of parity-time (PT)-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT-symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems

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3D parity-time (PT)-symmetric optical lattices are used to overcome the collapse of 3D ultracold atoms.

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3D matter-wave gap solitons and vortices are found in PT-symmetric optical lattices.

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Rich properties and dynamics of 3D matter-wave localized modes are disclosed.

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In-depth soliton physics is provided in 3D non-Hermitian periodic physical systems.

Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

Quantum information processing enhances human’s power to simulate nature in quantum level and solve complex problem efficiently. During the process, a series of operators is performed to evolve the system or undertake a computing task. In recent year, research interest in non-Hermitian quantum systems, dissipative-quantum systems and new quantum algorithms has greatly increased, which nonunitary operators take an important role in. In this work, we utilize the linear combination of unitaries technique for nonunitary dynamics on a single qubit to give explicit decompositions of the necessary unitaries, and simulate arbitrary time-dependent single-qubit nonunitary operator F(t) using duality quantum algorithm. We find that the successful probability is not only decided by F(t) and the initial state, but also is inversely proportional to the dimensions of the used ancillary Hilbert subspace. In a general case, the simulation can be achieved in both eight- and six-dimensional Hilbert spaces. In phase matching conditions, F(t) can be simulated by only two qubits. We illustrate our method by simulating typical non-Hermitian systems and single-qubit measurements. Our method can be extended to high-dimensional case, such as Abrams–Lloyd’s two-qubit gate. By discussing the practicability, we expect applications and experimental implementations in the near future.

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

Investigation of P T- and P T-antisymmetry in two dimensional (2D) optical lattices

A collection of cold rubidium atoms in three-level configuration trapped in two dimensional (2D) optical lattices is revisited. The trapped atoms are considered in the Gaussian density distribution and we study the realization of P T-, non-P T-, and P T-antisymmetry in 2D optical lattices. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, control over P T- to non-P T-symmetry and vice versa in 2D optical lattices is achieved via a single knob such as microwave field, probe field and relative phase of optical and microwave fields. In addition, control over P T-antisymmetry to non-P T-symmetry and vice versa is also achieved via relative phase. The coherent control of P T- non-P T- and P T-antisymmetry in optical susceptibility of 2D atomic lattices can be extended to 2D optical devices including modulators, detectors, and the 2D atomic lattices can also be extended to photonic transistors and diodes.

Coherent control of nonreciprocal reflections with spatial modulation coupling in parity-time symmetric atomic lattice

A collection of cold rubidium atoms in three-level configuration trapped in one dimensional (1D) optical lattice is revisited. The trapped atoms are considered in the Gaussian density distribution and study the realization of P T-, non-P T- and P T anti-symmetry in optical susceptibility in 1D atomic lattices in a periodic structure. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, a nonreciprocal optical propagation phenomenon is investigated. In this system, we have introduced a microwave that couples to the two ground states, spatial modulation of the coupling field, and the atomic density with Gaussian distribution in practice. With a proper detuning and coupling field Rabi frequencies, we can find the condition of P T-symmetry along with field propagation direction, and the novel properties of transmission and reflections have been discussed. The large difference of field reflections from the two ends of the atomic lattice medium shows strong evidence that the nonreciprocal behavior can be greatly enhanced by increasing the spatial modulation amplitude.

Transport properties of the non-Hermitian T-shaped quantum router

In this study, we design a T-shaped quantum router that comprises two-level systems (TLSs), an infinite coupled resonator waveguide (CRW), and a semi-infinite CRW. The loss (absorption) and gain (amplification) of the energy levels of the TLSs can be considered as energy exchange between the system and its environment. Considering loss in the ground state and gain in the excited state of the TLSs and loss of cavities, the system is non-energy-conserving and non-Hermitian. Loss in the system consists of loss of cavities and TLSs. The total transmission probabilities (TPs) of photons in the system are equal to 1 or lower when the system has loss only. Loss causes a bounce-back phenomenon in the TPs. The TPs have a divergent point when the TLSs have gain, and we obtain this divergent condition. The reflection probability has a minimal point only when photons are incident from the semi-infinite CRW and the system has loss. The TPs of the non-Hermitian router are increased by gain, decreased by loss, and conserved under certain conditions.

Lop-sided Raman-Nath diffraction in PT-antisymmetric atomic lattices

Two-dimensional (2D) optical lattices of driven cold atoms can provide a useful platform to construct 2D electromagnetically induced grating (EIG) with parity-time (PT) antisymmetry. This atomic grating is achieved by the spatial modulations of the atomic density and frequency detunings in the four-level double-Λ atomic system. Gain-assisted PT antisymmetry allows us to realize lop-sided Raman-Nath diffraction with high diffraction efficiency at the exception point. It is shown that the nontrivial phenomenon originates from non-Hermitian degeneracy of PT antisymmetry. Our scheme may provide the possibility for active all-optical control and conversion of the spatial beam in optics.

Parity-time symmetry in coherent asymmetric double quantum wells

A coherently prepared asymmetric double semiconductor quantum well (QW) is proposed to realize parity-time (PT) symmetry. By appropriately tuning the laser fields and the pertinent QW parameters, PT-symmetric optical potentials are obtained by three different methods. Such a coherent QW system is reconfigurable and controllable, and it can generate new approaches of theoretically and experimentally studying PT-symmetric phenomena.

Intrinsic link of asymmetric reflection and diffraction in non-Hermitian gratings

Asymmetric reflection in Bragg gratings and asymmetric diffraction in diffraction gratings are both linked to parity-time (PT) symmetry in non-Hermitian optics, but their direct relation has not been examined. To fill this gap, we first consider a PT-symmetric sinusoidal grating to compare the contrast of forward and backward reflectivities and the ratio of ±1-order diffraction efficiencies. Analytical and numerical results show that they change with identical tendencies and peaks at same positions in a wide parameter space, indicating thus an intrinsic link in both PT symmetric and PT broken phases. The underlying physics is found to be that the unbalanced coupling strengths between forward and backward reflected waves are identical to those between 0-order and ±1-order diffracted waves. We then consider a non-Hermitian grating dynamically induced in cold atomic lattices to include higher-order diffractions and corresponding reflections.Full numerical calculations show that the aforementioned findings hold also true in this complicated but practical grating, even in more general non-Hermitian cases beyond the exact PT symmetry.

Realization of simultaneously parity-time-symmetric and parity-time-antisymmetric susceptibilities along the longitudinal direction in atomic systems with all optical controls

We propose an all-optical-control scheme to simultaneously realize parity-time (𝒫𝒯)-symmetric and 𝒫𝒯-antisymmetric susceptibilities along the propagation direction of light by applying an external magnetic field. Through the light-atom interaction within a double-Λ configuration, the resulting position-dependent susceptibilities for the interacting fields can be manipulated through the relative phase between them. In particular, for the probe field, one can switch its refractive index from the 𝒫𝒯-symmetry to 𝒫𝒯-antisymmetry by just varying the phase. Based on the quantum interference among transition channels in a closed loop, analytical formulas are also derived to illustrate the conditions for 𝒫𝒯-symmetry and 𝒫𝒯-antisymmetry.

PT symmetry and antisymmetry by anti-Hermitian wave coupling and nonlinear optical interactions

Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of antiparity-time (PT) symmetry in optics. Remarkably, under a different definition of parity operator, a PT symmetry can be found as well in such systems. Such symmetries are ubiquitous in nonlinear optical interactions and are exemplified by considering modulation instability in optical fibers and optical parametric amplification.

Asymmetric light diffraction of an atomic grating with PT symmetry

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.

Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices

We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.