Four-level Quantum System Research Articles

Electromagnetically induced transparency and enhanced self-Kerr nonlinearity in a four-level scheme

We analyze the interaction of three laser fields with a four-level quantum system in a tripod configuration. We obtain an analytical expression for the linear susceptibility and nonlinear susceptibility of a weak-probe field and show that the properties of double electromagnetically induced transparency and the self-Kerr nonlinearity can be modified significantly by changing the ratio of the two coupling fields. We also show that a coherently prepared tripod scheme can be used for a giant self-Kerr nonlinearity generation with vanishing absorption in the case of optimal ratio. We present a physical understanding of our numerical results using the dressed-state approach and analytical explanation.

Multiphoton excitations and inverse population in a system of two flux qubits

We study spectroscopy of artificial solid-state four-level quantum system. This system is formed by two coupled superconducting flux qubits. When multiple driving frequency of the applied microwaves matches the energy difference between any two levels, the transition to the upper level is induced. We demonstrate two types of the multi-photon transitions: direct transitions between two levels and ladder-type transitions via an intermediate level. For the latter transitions, in particular, the inverse population of the excited state with respect to the ground one is realized. These processes can be useful for the control of the level population for the multilevel scalable quantum systems.

The Study of Quantum Interference in Metallic Photonic Crystals Doped with Four-Level Quantum Dots

In this work, the absorption coefficient of a metallic photonic crystal doped with nanoparticles has been obtained using numerical simulation techniques. The effects of quantum interference and the concentration of doped particles on the absorption coefficient of the system have been investigated. The nanoparticles have been considered as semiconductor quantum dots which behave as a four-level quantum system and are driven by a single coherent laser field. The results show that changing the position of the photonic band gap about the resonant energy of the two lower levels directly affects the decay rate, and the system can be switched between transparent and opaque states if the probe laser field is tuned to the resonance frequency. These results provide an application for metallic nanostructures in the fabrication of new optical switches and photonic devices.

COMPLEMENTARITY AND THE ALGEBRAIC STRUCTURE OF FOUR-LEVEL QUANTUM SYSTEMS

The history of complementary observables and mutual unbiased bases is shortly reviewed. A characterization is given in terms of conditional entropy of subalgebras due to Connes and Størmer. The extension of complementarity to noncommutative subalgebras is considered as well. Possible complementary decompositions of a four-level quantum system are described and a characterization of the Bell basis is obtained: The MASA generated by the Bell basis is complementary to both M2(ℂ) tensor factors.

On the waves of plastic flow localization in pure metals and alloys

In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equations on the basis of already known exact solutions of the one-spin equation. Besides, we present some exact solutions for the two-spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time-independent spin interaction and a time-independent external background. A possible analogue of the Rabi problem for the two-spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.

Two interacting spins in external fields. Four-level systems

In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equations on the basis of already known exact solutions of the one-spin equation. Besides, we present some exact solutions for the two-spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time-independent spin interaction and a time-independent external background. A possible analogue of the Rabi problem for the two-spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.

Realization of Four-Level Qudits Using Biphotons

The novel experimental realization of four-level optical quantum systems (ququarts) is presented. We exploit the polarization properties of the frequency nondegenerate biphoton field to obtain such systems. A simple method that does not rely on am interferometer is used to generate and measure the sequence of states that can be used in quantum key distribution protocol.

Transparency, slow light and enhanced nonlinear optics in a four-level scheme

We analyse the interaction of three laser fields with a four-level quantum system in a tripod configuration. We obtain an analytical expression for the steady state linear susceptibility of a probe laser field and show that the system can exhibit double electromagnetically induced transparency with controlled group velocity. We also show that a coherently prepared tripod scheme can be used for efficient nonlinear generation of new laser fields.

Transparency and parametric generation in a four-level system † Reviewing of this paper was handled by a member of the Editorial Board.

We analyse two distinct nonlinear phenomena in a four-level quantum system having a tripod configuration. First, we show that the system can become transparent at two different frequencies of a probe laser field. The potential for parametric generation in this medium is also investigated. We show that, if the system is prepared in a coherent superposition of two or three of the lower levels, one or two new fields can be generated.

Quantum simulation with natural decoherence

A quantum system may be efficiently simulated by a quantum information processor as suggested by Feynman and developed by Lloyd, Wiesner, and Zalka. Within the limits of the experimental implementation, simulation permits the design and control of the kinematic and dynamic parameters of a quantum system. Extension to the inclusion of the effects of decoherence, if approached from a full quantum-mechanical treatment of the system and the environment, or from a semiclassical fluctuating field treatment (Langevin), requires the difficult access to dynamics on the time scale of the environment correlation time. Alternatively, a quantum-statistical approach may be taken which exploits the natural decoherence of the experimental system, and requires a more modest control of the dynamics. This is illustrated for quantum simulations of a four-level quantum system by a two-spin NMR ensemble quantum information processor.

A self-guided algorithm for learning control of quantum-mechanical systems

This paper presents a general self-guided algorithm for direct laboratory learning of controls to manipulate quantum-mechanical systems. The primary focus is on an algorithm based on the learning of a linear laboratory input–output map from a sequence of controls, and their observed impact on the quantum-mechanical system. This map is then employed in an iterative fashion, to sequentially home in on the desired objective. The objective may be a target state at a final time, or a continuously weighted observational trajectory. The self-guided aspects of the algorithm are based on implementing a cost functional that only contains laboratory-accessible information. Through choice of the weights in this functional, the algorithm can automatically stay within the bounds of each local linear map and indicate when a new map is necessary for additional iterative improvement. Finally, these concepts can be generalized to include the possibility of employing nonlinear maps, as well as just the laboratory control instrument settings, rather than observation of the control itself. An illustrative simulation of the concepts is presented for the control of a four-level quantum system.

On the Population Loss Dynamics of a Strongly Excited Four-level System

Abstract The population dynamics of a strongly excited four-level quantum system with allowed loss out of the system from the highest state are analysed. This work has been stimulated by the paper of Cardimona et al. and represents a more general treatment of the problem studied by them. In particular, we show that the reduction in the ground-state population decay rate for large losses is not a consequence of the two-level behaviour but is a more general phenomenon. On the basis of numerical and analytical solutions we demonstrate that for an arbitrary excitation regime, at sufficiently large decay rate, the population loss dynamics of the four-level system is reduced to that of a slowly damped three-level system. We demonstrate also that the detailed knowledge of the coherent population dynamics enables us to predict the effect of decay rate on the population's time evolution for arbitrary choice of dynamic parameters.

Reduction of a strongly damped atomic four-level system to an effective three-level system

A three-laser excited four-level quantum system with allowed fast population loss from the highest state is considered. It is shown that the formal treatment of this system can be reduced to that of a weakly damped three-level system. Under definite conditions this reduction could be carried out analytically.

Signal and noise conversion in four-level quantum systems

Signal and noise conversion in four-level quantum systems