Steve MacLean

A scheme for the detection of mixing processes in vacuum

Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1(Dated: July 14, 2014)A scheme for the detection of photons generated by vacuum mixing processes is proposed. Thestrategy consists in the utilization of a high numerical aperture parabolic mirror which tightly fo-cuses two co-propagating laser beams with di erent frequencies. This produces a very high intensityregion in the vicinity of the focus, where the photon-photon nonlinear interaction can then inducenew electromagnetic radiation by wave mixing processes. These processes are investigated theoreti-cally. The eld at the focus is obtained from the Stratton-Chu vector di raction theory, which canaccomodate any con guration of an incoming laser beam. The number of photons generated is eval-uated for an incident radially polarized beam. It is demonstrated that using this eld con guration,vacuum mixing processes could be detected with envisaged laser technologies.

Pulse shape optimization for electron-positron production in rotating fields

We optimize the pulse shape and polarization of time-dependent electric fields to maximize the production of electron-positron pairs via strong field quantum electrodynamics processes. The pulse is parametrized in Fourier space by a B-spline polynomial basis, which results in a relatively low-dimensional parameter space while still allowing for a large number of electric field modes. The optimization is performed by using a parallel implementation of the differential evolution, one of the most efficient metaheuristic algorithms. The computational performance of the numerical method and the results on pair production are compared with a local multistart optimization algorithm. These techniques allow us to determine the pulse shape and field polarization that maximize the number of produced pairs in computationally accessible regimes.

Suppression of Multiphoton Resonances in Driven Quantum Systems via Pulse Shape Optimization

This Letter demonstrates control over multiphoton absorption processes in driven two-level systems, which include, for example, superconducting qubits or laser-irradiated graphene, through spectral shaping of the driving pulse. Starting from calculations based on Floquet theory, we use differential evolution, a general purpose optimization algorithm, to find the Fourier coefficients of the driving function that suppress a given multiphoton resonance in the strong field regime. We show that the suppression of the transition probability is due to the coherent superposition of high-order Fourier harmonics which closes the dynamical gap between the Floquet states of the two-level system.

Algorithm for the solution of the Dirac equation on digital quantum computers

A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the Dirac operator to a quantum walk supplemented by unitary rotation steps in spinor space. Every step of the splitting method is decomposed into sets of quantum gates. It is demonstrated that the algorithm has an exponential speedup over the implementation of the same numerical scheme on a classical computer, as long as certain conditions are satisfied. Finally, an explicit decomposition of this algorithm into elementary gates from a universal set is carried out to determine the resource requirements. It is shown that a proof-of-principle calculation may be possible with actual quantum technologies.

Coherent destruction of tunneling in graphene irradiated by elliptically polarized lasers

Photo-induced transition probabilities in graphene are studied theoretically from the viewpoint of Floquet theory. Conduction band populations are computed for a strongly, periodically driven graphene sheet under linear, circular, and elliptic polarization. Features of the momentum spectrum of excited quasi-particles can be directly related to the avoided crossing of the Floquet quasi-energy levels. In particular, the impact of the ellipticity and the strength of the laser excitation on the avoided crossing structure-and on the resulting transition probabilities-is studied. It is shown that the ellipticity provides an additional control parameter over the phenomenon of coherent destruction of tunneling in graphene, allowing one to selectively suppress multiphoton resonances.

Driven quantum tunneling and pair creation with graphene Landau levels

Driven tunneling between graphene Landau levels is theoretically linked to the process of pair creation from vacuum, a prediction of quantum electrodynamics (QED). Landau levels are created by the presence of a strong, constant, quantizing magnetic field perpendicular to a graphene mono-layer. Following the formal analogy between QED and the description of low-energy excitations in graphene, solutions of the fully interacting Dirac equation are used to compute electron-hole pair creation driven by a circularly or linearly polarized field. This is achieved via the coupled channel method, a numerical scheme for the solution of the time-dependent Dirac equation in the presence of bound states. The case of a monochromatic driving field is first considered, followed by the more realistic case of a pulsed excitation. We show that the pulse duration yields an experimental control parameter over the maximal pair yield. Orders of magnitude of the pair yield are given for experimentally achievable magnetic fields and laser intensities weak enough to preserve the Landau level structure.

Numerical Computation of Dynamical Schwinger-like Pair Production in Graphene

The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electric field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the calculation is performed within the strong field quantum electrodynamics formalism, requiring a solution of the Dirac equation in momentum space. The equation is solved using a split-operator numerical scheme on parallel computers, allowing for the investigation of several field configurations. The strength of the method is illustrated by computing the electron momentum density generated from a realistic laser pulse model. We observe quantum interference patterns reminiscent of Landau–Zener–Stückelberg interferometry.

Efficient state initialization by a quantum spectral filtering algorithm

An algorithm that initializes a quantum register to a state with a specified energy range is given, corresponding to a quantum implementation of the celebrated Feit-Fleck method. This is performed by introducing a nondeterministic quantum implementation of a standard spectral filtering procedure combined with an apodization technique, allowing for accurate state initialization. It is shown that the implementation requires only two ancilla qubits. A lower bound for the total probability of success of this algorithm is derived, showing that this scheme can be realized using a finite, relatively low number of trials. Assuming the time evolution can be performed efficiently and using a trial state polynomially close to the desired states, it is demonstrated that the number of operations required scales polynomially with the number of qubits. Tradeoffs between accuracy and performance are demonstrated in a simple example: the harmonic oscillator. This algorithm would be useful for the initialization phase of the simulation of quantum systems on digital quantum computers.

Efficiently parallelized modeling of tightly focused, large bandwidth laser pulses

The Stratton-Chu integral representation of electromagnetic fields is used to study the spatio-temporal properties of large bandwidth laser pulses focused by high numerical aperture mirrors. We review the formal aspects of the derivation of diffraction integrals from the Stratton-Chu representation and discuss the use of the Hadamard finite part in the derivation of the physical optics approximation. By analyzing the formulation we show that, for the specific case of a parabolic mirror, the integrands involved in the description of the reflected field near the focal spot do not possess the strong oscillations characteristic of diffraction integrals. Consequently, the integrals can be evaluated with simple and efficient quadrature methods rather than with specialized, more costly approaches. We report on the development of an efficiently parallelized algorithm that evaluates the Stratton-Chu diffraction integrals for incident fields of arbitrary temporal and spatial dependence. This method has the advantage that its input is the unfocused field coming from the laser chain, which is experimentally known with high accuracy. We use our method to show that the reflection of a linearly polarized Gaussian beam of femtosecond duration off a high numerical aperture parabolic mirror induces ellipticity in the dominant field components and generates strong longitudinal components. We also estimate that future high-power laser facilities may reach intensities of

Time-dependent pair creation and the Schwinger mechanism in graphene

10^{24}\,\text{W/cm}^2