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arXiv:1702.07833 · Physical Review A

Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit

Han-gyeol Lee, Yunheung Song, Jaewook Ahn

Published Jul 20, 2017• 5 citations
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Abstract

Arbitrary rotation of a qubit can be performed with a three-pulse sequence, for example, $ZYZ$ rotations. However, this requires precise control of the relative phase and timing between the pulses, making it technically challenging in optical implementation in a short time scale. Here we show any $ZYZ$ rotations can be implemented with a single laser pulse, that is, a chirped pulse with a temporal hole. The hole of this shaped pulse induces a nonadiabatic interaction in the middle of the adiabatic evolution of the chirped pulse, converting the central part of an otherwise simple $Z$ rotation to a $Y$ rotation, constructing $ZYZ$ rotations. The result of our experiment performed with shaped femtosecond laser pulses and cold rubidium atoms shows strong agreement with the theory.

DOI
10.1103/physreva.96.012326

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Arbitrary rotation of a qubit can be performed with a three-pulse sequence, for example, ZYZZYZZYZ rotations. However, this requires precise control of the relative phase and timing between the pulses, making it technically challenging in optical implementation in a short time scale. Here we show any ZYZZYZZYZ rotations can be implemented with a single laser pulse, that is, a chirped pulse with a temporal hole. The hole of this shaped pulse induces a nonadiabatic interaction in the middle of the adiabatic evolution of the chirped pulse, converting the central part of an otherwise simple ZZZ rotation to a YYY rotation, constructing ZYZZYZZYZ rotations. The result of our experiment performed with shaped femtosecond laser pulses and cold rubidium atoms shows strong agreement with the theory.
We show how one can perform arbitrary rotation of any qubit, using delayed laser pulses through nonadiabatic evolution, i.e., via transitions among the adiabatic states. We use a double-Lambda scheme and use a set of control parameters such as detuning, ratio of pulse amplitudes, time-separation of two pulses for realizing different rotations of the qubit. We also investigate the effect of different kinds of chirping, namely linear chirping and hyperbolic tangent chirping. Our work using nonadiabatic evolution adds to the flexibility in the implementation of logic gate operations and show how to achieve control of quantum systems by using different types of pulses.
Extremely fast qubit controls can greatly reduce the calculation time in quantum computation, and potentially resolve the finite-time decoherence issues in many physical systems. Here, we propose and experimentally demonstrate pico-second time-scale controls of atomic clock state qubits, using Berry-phase gates implemented with a pair of chirped laser pulses. While conventional methods of microwave or Raman transitions do not allow atomic qubit controls within a time faster than the hyperfine free evolution period, our approach of ultrafast Berry-phase gates accomplishes fast clock-state operations. We also achieves operational robustness against laser parametric noises, since geometric phases are determined by adiabatic evolution pathway only, without being affected by any dynamic details. The experimental implementation is conducted with two linearly polarized, chirped ultrafast optical pulses, interacting with five single rubidium atoms in an array of optical tweezer dipole traps, to demonstrate the proposed ultrafast clock-state gates and their operational robustness.
The most common method to implement quantum gates is based on the Rabi solution regime of a two-level system excited by external field. There is a very simple reason for this choice. To construct a quantum gate one needs to know the exact form of evolution operator of the qubit under the external excitation. In the case of Rabi solution the qubit evolution has very simple and easily interpreted form. In essence, the whole dynamics of the qubit wave function is governed by the pulse area and it exhibits Rabi oscillations for the time less than the decoherence time. Various implementations of the quantum gates employ relatively weak pulses that results in slow gate operations of order microseconds. To make quantum gates faster one may use strong femtosecond pulses. However, direct implementation schemes are not so obvious because of strong field effects and large bandwidth of the pulses might give rise to unwanted excitations. Here we propose a simple scheme which provides a possibility to utilize strong pulses while keep all advantages of Rabi solution regime. We design fast gates (picosecond time scale) by choosing proper parameters of the chirped pulses as a way to control nonadiabatic terms and to satisfy the adiabaticity conditions. Proposed Hadamard and phase-shift gate allow us to construct universal set of single qubit gates by controlling the effective pulse area and two-photon detuning. The proposed excitation scheme can be used to implement CNOT gate as well.
Quantum computing is based on unitary operations in a two-level quantum system, a qubit, as the fundamental building block, and the ability to perform qubit operations in an amount of time that is considerably shorter than the coherence time is an essential requirement for quantum computation. Here, we present an experimental demonstration of arbitrary single-qubit SU(2) quantum gate operations achieved at a terahertz clock speed. Implemented by coherent control methods of tailored ultrafast laser interaction with cold rubidium atomic qubits, Bloch vector manipulation about all three rotational axes was successfully demonstrated. The dynamic evolution of the qubits was successfully measured by devised femtosecond Ramsey interferometry. We anticipate this demonstration to be a starting point to process quantum algorithm in a simplified manner by a programmed sequence of femtosecond laser pulses.
Semiconductor quantum dots have been featured in a number of proposals for quantum computing because of the advantages afforded by confinement on the nanoscale, such as well separated, discrete energy levels and ease of optical manipulation. In addition, they can leverage established semiconductor fabrication techniques and, like the quantum dots used in this work, can be designed to match the telecommunication band, improving the scalability and potential integration of the platform into existing technologies. This thesis work applied optical pulse engineering to manipulate exciton qubits in self-assembled InAs quantum dots. Optimal quantum control theory was used to design pulse shapes that implement high fidelity single-qubit and two-qubit operations, with constraints on the numerical optimization that ensure that the pulses can be accurately implemented using a commercial 4f pulse shaper. In the case of single-qubit operations, the results showed that two uncoupled qubits can be manipulated in parallel using a single phase-shaped laser pulse, provided their optoelectronic properties are sufficiently different. It was demonstrated that targeted differences in inversion and phase between the qubits can be achieved on an ultrafast timescale with high fidelity. In the case of two-qubit operations, the controlled-rotation gate was optimized using amplitude-only and phase-only pulse shaping schemes. The shaped pulses for both schemes were shown to produce higher fidelity operations. The ability to implement robust state inversion on short timescales is particularly useful for technologies such as ultrafast optical switches, single-photon sources, and entangled-photon sources. This work has demonstrated state inversion in a single InAs quantum dot via adiabatic rapid passage using linearly chirped laser pulses. The achieved gate times were an order of magnitude shorter than previous demonstrations. Theoretical predictions of the dependence of the inversion efficiency of the exciton on the sign of the pulse chirp were also verified experimentally, allowing for the identification of phonon-mediated dephasing as the dominant source of decoherence.
We demonstrate subpicosecond-timescale population transfer between the pair of hyperfine ground states of atomic rubidium using a single laser-pulse. Our scheme utilizes the geometric and dynamic phases induced during Rabi oscillation through the fine-structure excited state to construct an XXX rotation gate for the hyperfine-state qubit system. The experiment performed with a femtosecond laser and cold rubidium atoms, in a magnetooptical trap, shows over 98% maximal population transfer between the clock states.