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Physical Review A

Transparent control of an exactly solvable two-level system via combined modulations

Wenhua Hai, Kuo Hai, Qiong Chen

Published Feb 8, 2013• 20 citations
Publisher

Abstract

Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.

DOI
10.1103/physreva.87.023403

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Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.
We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling, and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.
Analytical solutions to the time-dependent Schrödinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions. Any function satisfying these constraints yields an exact analytical solution. We demonstrate this method by presenting several new exact solutions to the time-dependent Schrödinger equation. Our general method and many of the new solutions we present are particularly relevant to qubit control in quantum computing applications.
Abstract Exact solutions for spin-orbit (SO)-coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the exactly analytic solutions for a single SO-coupled ultracold atom held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the generally accurate solutions of this system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the specially exact solutions in simple form when the driving parameters are appropriately chosen. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary coherent population transfer with and/or without spin-flipping, the controlled coherent population conservation, and the controlled coherent population inversion. The results may provide a possibility for generating the accurate quantum entangled states and the exact control of spin dynamics for a SO-coupled ultracold atomic system.
Exact solutions for spin-orbit (SO) coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the analytic exact solutions for an SO-coupled boson held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the general analytical accurate solutions of the system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the special exact solutions in simple form when the driving parameters satisfy certain conditions. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary population transfer (APT) with and/or without spin-flipping, the controlled coherent population conservation (CCPC), and the controlled coherent population inversion (CCPI). The results may have potential applications in the preparation of accurate quantum entangled states and quantum information processing.
Abstract We present a new approach for generating arbitrary analytically solvable two-level systems. This method offers the ability to completely derive all analytically solvable Hamiltonians for any analytical evolutions of two-level systems. To demonstrate the effectiveness of this approach, we reconstruct the Rosen–Zener model and generate several new exact solutions. Using this approach, we present the exact evolution of the semi-classical Rabi model with new analytical properties. The parameters used to generate Hamiltonians have direct physical interpretations within the Bloch sphere, the quantum speed limit, and the geometric phase. As a result, the physical properties of the generated Hamiltonian are highly controllable, which plays a significant role in the fields of quantum control, quantum computing, and quantum information.
Abstract It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases, even for two-level quantum systems. Thus, finding the exact quantum dynamics under a time-dependent Hamiltonian is not only fundamentally important in quantum physics but also facilitates active quantum manipulations for quantum information processing. In this work, we present a method for generating nearly infinite analytically assisted solutions to the Schrödinger equation for a qubit under time-dependent driving. These analytically assisted solutions feature free parameters with only boundary restrictions, making them applicable in a variety of precise quantum manipulations. Due to the general form of the time-dependent Hamiltonian in our approach, it can be readily implemented in various experimental setups involving qubits. Consequently, our scheme offers new solutions to the Schrödinger equation, providing an alternative analytical framework for precise control over qubits.