3,115 research outputs found
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 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
. 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
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 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 W output power is feasible as the
signal absorption in undoped superlattices is negligible.Comment: 3pages 2figure
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.
No-go theorem and optimization of dynamical decoupling against noise with soft cutoff
We study the performance of dynamical decoupling in suppressing decoherence
caused by soft-cutoff Gaussian noise, using short-time expansion of the noise
correlations and numerical optimization. For the noise with soft cutoff at high
frequencies, there exists no dynamical decoupling scheme to eliminate the
decoherence to arbitrary orders of the short time, regardless of the timing or
pulse shaping of the control under the population conserving condition. We
formulate the equations for optimizing pulse sequences that minimizes
decoherence up to the highest possible order of the short time for the noise
correlations with odd power terms in the short-time expansion. In particular,
we show that the Carr-Purcell-Meiboom-Gill sequence is optimal in short-time
limit for the noise correlations with a linear order term in the time
expansion.Comment: 11 pages, 3 figure
Faraday rotation echo spectroscopy and detection of quantum fluctuations
Central spin decoherence is useful for detecting many-body physics in
environments and moreover, the spin echo control can remove the effects of
static thermal fluctuations so that the quantum fluctuations are revealed. The
central spin decoherence approach, however, is feasible only in some special
configurations and often requires uniform coupling between the central spin and
individual spins in the baths, which are very challenging in experiments. Here,
by making analogue between central spin decoherence and depolarization of
photons, we propose a scheme of Faraday rotation echo spectroscopy (FRES) for
studying quantum fluctuations in interacting spin systems. The echo control of
the photon polarization is realized by flipping the polarization with a
birefringence crystal. The FRES, similar to spin echo in magnetic resonance
spectroscopy, can suppress the effects of the static magnetic fluctuations and
therefore reveal dynamical magnetic fluctuations. We apply the scheme to a
rare-earth compound LiHoF4 and calculate the echo signal, which is related to
the quantum fluctuations of the system. We observe enhanced signals at the
phase boundary. The FRES should be useful for studying quantum fluctuations in
a broad range of spin systems, including cold atoms, quantum dots, solid-state
impurities, and transparent magnetic materials
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