Berry phases of quantum trajectories in semiconductors under strong terahertz fields

Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to understand extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz sideband generation (HSG). While HHG and ATI have been mostly studied in atoms and molecules, the HSG in semiconductors can have interesting effects due to possible nontrivial "vacuum" states of band materials. We find that in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field can accumulate Berry phases. Taking monolayer MoS$_2$ as a model system, we show that the Berry phases appear as the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.Comment: 5 page

Dynamical decoupling for a qubit in telegraph-like noises

Based on the stochastic theory developed by Kubo and Anderson, we present an exact result of the decoherence function of a qubit in telegraph-like noises under dynamical decoupling control. We prove that for telegraph-like noises, the decoherence can be suppressed at most to the third order of the time and the periodic Carr-Purcell-Merboom-Gill sequences are the most efficient scheme in protecting the qubit coherence in the short-time limit.Comment: 4 page

Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators

We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related to the integration of the non-Abelian Berry curvature over the Brillouin zone. We apply the result to insulators with rotational symmetry near the band edge. Under resonant excitations, the optical susceptibility is proportional to the flux of the Berry curvature through the iso-energy surface, which is equal to the Chern number of the surface times $2\pi$. For the III-V compound semiconductors, microscopic calculations based on the six-band model give a third-order susceptibility with the Chern number of the iso-energy surface equal to three

Imaginary geometric phases of quantum trajectories

A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also experience dephasing, or quantum diffusion. Here we show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we study the quantum trajectories of the optically excited electron-hole pairs, driven by an elliptically polarized terahertz field, in a material with non-zero Berry curvature near the energy band extremes. While the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands. This discovery of geometric quantum diffusion extends the concept of geometric phases.Comment: 5 pages with 3 figure

Cosmology emerging as the gauge structure of a nonlinear quantum system

Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems, which often present exotic features, are particularly interesting. While quantum systems are intrinsically linear due to the superposition principle, nonlinear quantum mechanics can arise as an effective theory for interacting systems (such as condensates of interacting bosons). Here we show that gauge structures similar to curved spacetime can arise in nonlinear quantum systems where the superposition principle breaks down. In the canonical formalism of the nonlinear quantum mechanics, the geometric phases of quantum evolutions can be formulated as the classical geometric phases of a harmonic oscillator that represents the Bogoliubov excitations. We find that the classical geometric phase can be described by a de Sitter universe. The fundamental frequency of the harmonic oscillator plays the role of the cosmic scale factor and the classical geometric phase is an integral of a differential angle 2-form, which is half of the curvature 2-form of the associated de Sitter universe. While the gauge structure of a linear quantum system presents monopole singularity at energy level degeneracy points, nonlinear quantum systems, corresponding to their quantum critical surfaces in the parameter spaces, exhibits a conic singularity in their gauge structure, which mimics the casual singularity at the big bang of the de Sitter universe. This finding opens up a new approach to studying the gauge and topological structures of interacting quantum systems and sets up a new stage for quantum simulation of fundamental physics

Hyper-parallel photonic quantum computation with coupled quantum dots

It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility of achieving scalable hyper-parallel quantum computation based on two DOFs of photon systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both the spatial-mode and the polarization DOFs of a two-photon system simultaneously, by exploiting the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics (QED). This hyper-CNOT gate is implemented by manipulating the four qubits in the two DOFs of a two-photon system without auxiliary spatial modes or polarization modes. It reduces the operation time and the resources consumed in quantum information processing, and it is more robust against the photonic dissipation noise, compared with the integration of several cascaded CNOT gates in one DOF.Comment: 11 pages, 4 figures, one colum

Tunable terahertz emission from difference-frequency in biased superlattices

The terahertz emission from difference-frequency in biased superlattices is calculated with the excitonic effect included. Owing to the doubly resonant condition and the excitonic enhancement, the typical susceptibility can be as large as $10^{-5}$ m/V. The doubly resonant condition can always be realized by adjusting the bias voltage and the laser frequencies, thus the in-situ tunable emission is efficient in a range of several terahertz. Continuous wave operation with 1% quantum efficiency and $\mu$W output power is feasible as the signal absorption in undoped superlattices is negligible.Comment: 3pages 2figure

Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities

Hyperentanglement has attracted much attention for its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatial-polarization mixed hyperentangled Bell state with the errors in both the spatial mode and polarization DOFs, resorting to the nonlinear optics of a nitrogen-vacancy (NV) center in a diamond embedded in a photonic crystal cavity coupled to a waveguide. We present the first hyperentanglement purification protocol for purifying a pair of two-photon systems in a mixed hyperentangled Bell state with the errors in two DOFs. Besides, we propose an efficient hyperentanglement concentration protocol for a partially hyperentangled Bell pure state, which has the maximal success probability in principle. These two protocols are useful in long-distance quantum communication with hyperentanglementComment: 8 pages, 5 figures, two column

Quantum coherence induced second plateau in high-sideband generation

Optically excited electron-hole pairs, driven by a strong terahertz (THz) field, create high-sidebands in the optical spectrum. The sideband spectrum exhibits a 'plateau' up to a cutoff of 3.17Up, where Up is the ponderomotive energy. This cutoff is determined, semi-classically, from the maximum kinetic energy an electron-hole pair can gain from the THz field along a closed trajectory. A full quantum treatment reveals a second, classically forbidden, plateau with a cutoff of 8Up, the maximum kinetic energy an electron-hole pair can gain from the THz field along an open trajectory. The second plateau appears because a spatially separated electron and hole can still recombine if the classical excursion is within the coherence length of the electron-hole wavefunction or, equivalently, the coherence time is longer than the excursion time (half the THz field period). This effect broadens the range of materials and excitation conditions where high-sideband generations can occur, thereby providing a wealth of novel systems for ultrafast electro-optical applications.Comment: Updated to journal version with revised figure 1. 5 pages, 3 figure

Nonlinear optics of semiconductors under an intense terahertz field

A theory for nonlinear optics of semiconductors in the presence of an intense terahertz electric field is constructed based on the double-line Feynman diagrams, in which the nonperturbative effect of the intense terahertz field is fully taken into account through using the Floquet states as propagating lines in the Feynman diagrams.Comment: 5pages 1 figure, accepted by Phys. Rev.