AN ALGEBRAIC APPROACH TO THE INTERACTION OF A THREE-LEVEL ATOM INTERACTING WITH QUANTIZED RADIATION FIELD

2000 ◽  
Vol 14 (14) ◽  
pp. 1459-1471
Author(s):  
XU-BO ZOU ◽  
JING-BO XU ◽  
XIAO-CHUN GAO ◽  
JIAN FU
Keyword(s):  
Algebraic Structure ◽  
Evolution Operator ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Time Evolution Operator ◽  
Level Atom ◽  
Unitary Transformations ◽  
Quantized Field ◽  
Quantized Radiation Field ◽  
Multiphoton Interaction

The system of a three-level atom in the Ξ configuration coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time evolution operator for the system. Based on this su(3) structure, we also show that the system of a three-level atom in the Ξ configuration can be exactly transformed to an effective two-level Hamiltonian by an unitary transformation. Finally, we show that there exist an su (N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.

scholarly journals Two-level atom in a cross cavity

2013 ◽  
Vol 23 ◽  
pp. 31-34
Author(s):  
J. C. García-Melgarejo ◽  
J. J. Sánchez-Mondragón ◽  
K. J. Sánchez-Pérez ◽  
O. S. Magaña-Loaiza
Keyword(s):  
Wave Function ◽  
Electromagnetic Fields ◽  
Canonical Transformation ◽  
Evolution Operator ◽  
Atomic Inversion ◽  
Time Evolution Operator ◽  
Level Atom ◽  
Weak Intensity ◽  
Cavity Configuration ◽  
Intensity Regime

In this work we propose a model to analyze the interaction of a two-level atom (TLA) placed in a cross cavity configuration interacting with two electromagnetic fields injected within the cavity. A canonical transformation for field operators is proposed to obtain ef­fective Hamiltonian such as that of Jaynes-Cummings and we calculate the wave function via time-evolution operator. We present results for the atomic inversion for a state in the weak intensity regime.

scholarly journals Complexity growth in integrable and chaotic models

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Matthew DeCross ◽  
Arjun Kar ◽  
Yue Li ◽  
Onkar Parrikar
Keyword(s):  
Time Evolution ◽  
Evolution Operator ◽  
Linear Growth ◽  
Conjugate Points ◽  
Majorana Fermions ◽  
Time Evolution Operator ◽  
Free Theory ◽  
Group Manifold ◽  
Geodesic Length ◽  
Evolution Trajectory

Abstract We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($$ \sqrt{N} $$ N ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

Introduction, generation and entanglement of entangled displaced even and odd squeezed states

2021 ◽  
pp. 2050047
Author(s):  
Amir Karimi
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Squeezed States ◽  
Displacement Operator ◽  
Text Type ◽  
Level Atom ◽  
Displacement Parameter ◽  
Entangled Quantum States ◽  
Quantized Field ◽  
Classical Fields

In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.

Schmidt decomposition in the interaction of a three-level atom and a quantized field

2018 ◽  
Vol 72 (10) ◽  
Author(s):  
Jorge A. Anaya-Contreras ◽  
Arturo Zúñiga-Segundo ◽  
Aldo Espinosa-Zúñiga ◽  
Francisco Soto-Eguibar ◽  
Héctor M. Moya-Cessa
Keyword(s):  
Schmidt Decomposition ◽  
Level Atom ◽  
Quantized Field

scholarly journals Preparation of Approximate Eigenvector by Unitary Operations on Eigenstate in Abrams-Lloyd Quantum Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Latha S. Warrier
Keyword(s):  
Time Evolution ◽  
Programming Language ◽  
Spin Chain ◽  
Evolution Operator ◽  
Unitary Operator ◽  
Language Model ◽  
Quantum Algorithm ◽  
Basis Vector ◽  
Unitary Matrix ◽  
Time Evolution Operator

The Abrams-Lloyd quantum algorithm computes an eigenvalue and the corresponding eigenstate of a unitary matrix from an approximate eigenvector Va. The eigenstate is a basis vector in the orthonormal eigenspace. Finding another eigenvalue, using a random approximate eigenvector, may require many trials as the trial may repeatedly result in the eigenvalue measured earlier. We present a method involving orthogonalization of the eigenstate obtained in a trial. It is used as the Va for the next trial. Because of the orthogonal construction, Abrams-Lloyd algorithm will not repeat the eigenvalue measured earlier. Thus, all the eigenvalues are obtained in sequence without repetitions. An operator that anticommutes with a unitary operator orthogonalizes the eigenvectors of the unitary. We implemented the method on the programming language model of quantum computation and tested it on a unitary matrix representing the time evolution operator of a small spin chain. All the eigenvalues of the operator were obtained sequentially. Another use of the first eigenvector from Abrams-Lloyd algorithm is preparing a state that is the uniform superposition of all the eigenvectors. This is possible by nonorthogonalizing the first eigenvector in all dimensions and then applying the Abrams-Lloyd algorithm steps stopping short of the last measurement.

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