A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.
A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.
The problem of controlling the quantum state of a system is investigated using a time varying potential. As a concrete example we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We derive an analytic expression for the frequencies of resonance between states, and against standard intuition, we show how to use this behavior to control the quantum state of the system at will. In particular, we offer as an example the transition from the ground state to the first excited state of the square well potential. At first sight, it may be counter intuitive that we can control the state of such a quantum Hamiltonian, as the Schrödinger equation conserves the norm of the wave function. In this manuscript, we show how that can be achieved.
We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate-frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well-defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multilevel systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model.
Population inversion from an initial quantum state to a desired quantum state represents an exciting new frontier for quantum manipulation; that frontier is endowed with a strong interdisciplinary character and connections to other scientific fields, including atomic, molecular, and optical physics, as well as in solid-state devices, for fundamental studies, nuclear magnetic resonance and other spectroscopic techniques, metrology, interferometry, optical control of chemical reactions or quantum-information applications. Two-level systems are ubiquitous in these areas, and the driving of a population inversion is an important operation. So far various schemes for population transfer to a target state from an initial state have been proposed in theory and implemented in experiment. To be useful, such methods must, of course, be reliable, fast, and robust. Most literatures on two-level models investigated population inversion, which could be modelled by infinite-time processes. In this paper, by using a composite adiabatic passage (CAP) technique—in which the single pulse driving the quantum transition is replaced by a sequence of pulses with well-defined control phases, we investigate the population inversion problem of two-level quantum system with a finite duration. We take a sinusoidally varying pulse model that continuously vanishes at the beginning and the end of the finite duration as an example. The high-fidelity population inversion of the two-level system with finite duration is achieved. We discuss the effects of both coupling strength and detuning strength on the transition probability. It is found that this protocol could suppress the oscillations in the transition probability and reduce the admissible error bellow the 10 -4 quantum computation benchmark. The fidelity can arrive at 1, even with simple three- and five-composite pulse sequences. The protocol combines the advantages of adiabatic passage and composite pulses techniques. By choosing the composite phases appropriately, a high-fidelity, fast, stable and extremely robust complete population inversion is achieved for the finite-time two-level model. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp as long as the latter satisfy the symmetry property. Furthermore, the classical Hamiltonian is applied to describe the dynamic properties of the quantum system and further verify the effectiveness and feasibility of the proposed CAP technique. The results we present here are general and in principle apply to any two- and multi-level quantum systems. The accuracy of the CAP technique and its robustness against parameter variations make the protocol suitable for ultrahigh-fidelity quantum manipulation. We believe that the protocol can be widely used in many different areas of science, ranging from the quantum information, the quantum chemical, and the quantum optics to the ultracold atomic and molecular physics.
Transferring a quantum system to a final state with given populations is an important problem with applications to quantum chemistry and atomic physics. In this paper, we consider such transfers that minimize L2the norm of the control. This problem is challenging, both analytically and numerically. With the exception of the simplest cases, there is no general understanding of the nature of optimal controls and trajectories. We find that, by examining the limit of large transfer times, we can uncover such general properties. In particular, for transfer times large with respect to the time scale of the free dynamics of the quantum system, the optimal control is a sum of terms, each being a Bohr frequency sinusoid modulated by a slow amplitude, i.e., a profile that changes considerably only on the scale of the transfer time. Moreover, we show that the optimal trajectory follows a ldquomeanrdquo evolution modulated by the fast free dynamics of the system. The calculation of the ldquomeanrdquo optimal trajectory and the slow control profiles is done via an ldquoaveragedrdquo two-point boundary value problem that we derive and which is much easier to solve than the one expressing the necessary conditions for optimality of the original optimal transfer problem.
The difficulty in combining high fidelity with fast operation times and robustness against sources of noise is the central challenge of most quantum control problems, with immediate implications for the realization of quantum devices. We theoretically propose a protocol, based on the widespread stimulated Raman adiabatic passage technique, which achieves these objectives for quantum state transfers in generic three-level systems. Our protocol realizes accelerated adiabatic following through the application of additional control fields on the optical excitations. These act along frequency sidebands of the principal adiabatic pulses, dynamically counteracting undesired transitions. The scheme facilitates experimental control, not requiring new hardly-accessible resources. We show numerically that the method is efficient in a very wide set of control parameters, bringing the timescales closer to the quantum speed limit, also in the presence of environmental disturbance. These results hold for complete population transfers and for many applications, e.g., for realizing quantum gates, both for optical and microwave implementations. Furthermore, extensions to adiabatic passage problems in more-level systems are straightforward.
Abstract We have proposed and demonstrated a fast and robust method of population transfer between two quantum states using a quadratically chirped laser source. Numerically solving the time-dependent Schrödinger equation, transition probabilities have been obtained and the condition of the adiabatic passage is investigated. In this scheme, the wavelength of a laser source is quadratically swept in time to arbitrarily engineer the transition probabilities. The results show that complete and robust population transfer could be achieved by appropriate adjusting of the system parameters including the laser chirping parameter, the center frequency, and the coupling strength. Using this method, the time of the complete transition could be drastically decreased compared to the incorporation of the traditional linearly chirped laser.