Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInfinite quantum well: a coherent state approach
140
0
0.0
(
0
)
Added by
Pedro Garcia de Leon
Publication date
2008
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in this potential. We then study the resulting position and (well-defined) momentum operators. We also consider their mean values in coherent states and their quantum dispersions.
rate research
Read More
Machine learning (ML) has become an attractive tool in information processing, however few ML algorithms have been successfully applied in the quantum domain. We show here how classical reinforcement learning (RL) could be used as a tool for quantum state engineering (QSE). We employ a measurement based control for QSE where the action sequences are determined by the choice of the measurement basis and the reward through the fidelity of obtaining the target state. Our analysis clearly displays a learning feature in QSE, for example in preparing arbitrary two-qubit entangled states. It delivers successful action sequences, that generalise previously found human solutions from exact quantum dynamics. We provide a systematic algorithmic approach for using RL algorithms for quantum protocols that deal with non-trivial continuous state (parameter) space, and discuss on scaling of these approaches for preparation of arbitrarily large entangled (cluster) states.
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the {interference energy spectrum} of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction $Psi(x,t)$ with $N$ known zeros located at points $s_i = (x_i, t_i)$. Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particles quantum state is examined.
A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically enlarged. At specific, periodically recurring, times the particle can be found with probability one at the opposite end of the enlarged chamber in an interval of the same size as the initial well. With the help of symmetry considerations these times are calculated and shown to be dependent on the mass of the particle and the size of the enlarged chamber. Parameter ranges are given, where the non-relativistic nature of standard quantum mechanics becomes particularly apparent.
We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitions are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.
We exploit a novel approximation scheme to obtain a new and compact formula for the parameters underlying coherent-state control of the evolution of a pair of entangled two-level systems. It is appropriate for long times and for relatively strong external quantum control via coherent state irradiation. We take account of both discrete-state and continuous-variable degrees of freedom. The formula predicts the relative heights of entanglement revivals and their timing and duration.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
