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arXiv:1709.00652 · Physical Chemistry Chemical Physics

Optimal and robust control of quantum state transfer by shaping the spectral phase of ultrafast laser pulses

Yu Guo, Daoyi Dong, Chuan‐Cun Shu

Published Jan 1, 2018• 36 citations
arXivHTMLPDF

Abstract

Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.

DOI
10.1039/c8cp00512e

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Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.
The control of quantum dynamics via specially tailored laser pulses is a long-standing goal in physics and chemistry. Partly, this dream has come true, as sophisticated pulse-shaping experiments allow us to coherently control product ratios of chemical reactions. The theoretical design of the laser pulse to transfer an initial state to a given final state can be achieved with the help of quantum optimal control theory (QOCT). This tutorial provides an introduction to QOCT. It shows how the control equations defining such an optimal pulse follow from the variation of a properly defined functional. We explain the most successful schemes to solve these control equations and show how to incorporate additional constraints in the pulse design. The algorithms are then applied to simple quantum systems and the obtained pulses are analysed. Besides the traditional final-time control methods, the tutorial also presents an algorithm and an example to handle time-dependent control targets.
We present an optimal and robust quantum control method for efficient population transfer in asymmetric double quantum-dot molecules. We derive a long-duration control scheme that allows for highly efficient population transfer by accurately controlling the amplitude of a narrow-bandwidth pulse. To overcome fluctuations in control field parameters, we employ a frequency-domain quantum optimal control theory method to optimize the spectral phase of a single pulse with broad bandwidth while preserving the spectral amplitude. It is shown that this spectral-phase-only optimization approach can successfully identify robust and optimal control fields, leading to efficient population transfer to the target state while concurrently suppressing population transfer to undesired states. The method demonstrates resilience to fluctuations in control field parameters, making it a promising approach for reliable and efficient population transfer in practical applications.
We investigate two classes of quantum control problems by using frequency-domain optimization algorithms in the context of ultrafast laser control of quantum systems. In the first class of problems, the system model is known and a frequency-domain gradient-based optimization algorithm is applied for searching an optimal control field to selectively and robustly manipulate the population transfer in atomic rubidium. The other class of quantum control problems involves an experimental system with an unknown model. In this case, we introduce a differential evolution algorithm with a mixed strategy to search for optimal control fields and demonstrate the capability in an ultrafast laser control experiment for the fragmentation of Pr(hfac)3molecules.
Optimal control of quantum systems with complex constrained external fields is one of the longstanding theoretical and numerical challenges at the frontier of quantum control research. Here, we present a theoretical method that can be utilized to optimize the control fields subject to multiple constraints while guaranteeing monotonic convergence towards desired physical objectives. This optimization method is formulated in the frequency domain in line with the current ultrafast pulse shaping technique, providing the possibility for performing quantum optimal control simulations and experiments in a unified fashion. For illustrations, this method is successfully employed to perform multiple constraint spectral-phase-only optimization for maximizing resonant multiphoton transitions with desired pulses.
Creating and controlling well-defined single-photon states is important for many quantum enhanced technologies. Information can be encoded in any degree of freedom associated with a single-photon field excitation, for example in the polarization or transverse spatial mode structure. The ability to encode multiple qubits in these states is desirable for high data transmission rates and increased information processing capacity. The spectral-temporal domain offers a large Hilbert space for encoding information, well suited to integrated optical architectures owing to the low cross-talk between channels. Indeed, time-frequency encoding is an integral component of existing information technologies infrastructure. Thus, complete, coherent control of the spectral-temporal mode structure of light is essential to advancing optical quantum technologies. Arbitrary control of single-photon states has been demonstrated in the polarization and spatial-momentum degrees of freedom however, is yet to be established in the spectral-temporal domain. Recently it was shown that spectral-temporal pulse shaping is experimentally feasible using nonlinear optical methods. However, such techniques can introduce noise photons, are challenging to implement deterministically and require specially prepared auxiliary pump pulses. Furthermore, they are typically only possible at relatively low repetition rates to avoid damage of nonlinear optical materials. Here, we demonstrate deterministic pulse shaping of single-photon wave packets by introducing a time-varying phase. Applying linear or quadratic phase to the wave packet introduces a spectral shift or spectral broadening, respectively. Achieving significant spectral manipulation requires temporal-phase modulation on the order of π. The phase must also vary on the same time scale as the optical pulses, approximately 1 ps in duration here. This relatively rapid phase variation is achieved using a fast electro-optic phase modulator. The modulator is driven by a time-varying voltage that is synchronized with a pulse train of single-photon wave packets for accurate temporal phase control. In this thesis, we experimentally demonstrate control of the spectral-temporal state of single-photon wave packets using this method. Heralded single-photon wave packets are generated by spontaneous parametric down conversion pumped by a frequency-doubled Titanium-Sapphire laser oscillator with 80 MHz repetition rate. To achieve significant modulation of single-photon pulses a 10 V peak-to-peak radio-frequency signal of 40 GHz drives the phase modulator, which requires approximately 3.6 V to achieve a π phase shift. The signal is synchronized with the oscillator pulse train using custom designed electronics. Details of these electronics are presented, resulting in a robust phase and amplitude controllable 40 GHz voltage source, phase locked to the single-photon pulse train. To demonstrate the utility of this pulse-shaping method we experimentally show spectral shearing of almost 1 nm for single-photon wave packets with 830 nm central wavelength and 1 nm bandwidth. Measurement of the second-order intensity correlation before and after the wave-packet manipulation remains constant within uncertainty of the measurement, showing that the quantum nature of the single-photon source is not deteriorated by the modulator. Preservation of the wave-packet coherence is verified by two-photon interference between spectrally sheared and non-modulated single-photons.
Abstract A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stage of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single photon while maintaining the perfect state transfer. The key idea is twofold; (i) the control signal is allowed to vary continuously in time to introduce an additional degree of freedom, and then (ii) an optimal control problem is formulated to design a simple-formed input pulse and the corresponding control signal. Numerical simulations are conducted for Λ-type atomic media and networked atomic ensembles, to show the effectiveness of the proposed method.