83 research outputs found
A squeeze-like operator approach to position-dependent mass in quantum mechanics
We provide a squeeze-like transformation that allows one to remove a position
dependent mass from the Hamiltonian. Methods to solve the Schr\"{o}dinger
equation may then be applied to find the respective eigenvalues and
eigenfunctions. As an example, we consider a position-dependent-mass that leads
to the integrable Morse potential and therefore to well-known solutions
Coherent delocalization: Views of entanglement in different scenarios
The concept of entanglement was originally introduced to explain correlations
existing between two spatially separated systems, that cannot be described
using classical ideas. Interestingly, in recent years, it has been shown that
similar correlations can be observed when considering different degrees of
freedom of a single system, even a classical one. Surprisingly, it has also
been suggested that entanglement might be playing a relevant role in certain
biological processes, such as the functioning of pigment-proteins that
constitute light-harvesting complexes of photosynthetic bacteria. The aim of
this work is to show that the presence of entanglement in all of these
different scenarios should not be unexpected, once it is realized that the very
same mathematical structure can describe all of them. We show this by
considering three different, realistic cases in which the only condition for
entanglement to exist is that a single excitation is coherently delocalized
between the different subsystems that compose the system of interest
Multiphoton processes via conditional measurements in the two-field interaction
In this contribution, we show that the use of conditional measurements in the
resonant interaction of two quantized electromagnetic fields gives rise to
nonclassical multiphoton processes. Furthermore, we demonstrate that this
phenomenon may enable a robust integrated-optics protocol to engineer quantum
states containing a high number of photons, thus making it a potentially
appealing platform for exploring mesoscopic quantum phenomena.Comment: 12 pages, 6 figure
Temporal evolution of a driven optomechanical system in the strong coupling regime
We obtain a time-evolution operator for a forced optomechanical quantum
system using Lie algebraic methods when the normalized coupling between the
electromagnetic field and a mechanical oscillator, , is not
negligible compared to one. Due to the forcing term, the interaction picture
Hamiltonian contains the number operator in the exponents, and in order to deal
with it, we approximate these exponentials by their average values taken
between initial coherent states. Our approximation is justified when we compare
our results with the numerical solution of the number of photons, phonons,
Mandel parameter, and the Wigner function, showing an excellent agreement.Comment: 21 pages, 11 figure
The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values
A which-way measurement destroys the twin-slit interference pattern. Bohr
argued that distinguishing between two slits a distance s apart gives the
particle a random momentum transfer \wp of order h/s. This was accepted for
more than 60 years, until Scully, Englert and Walther (SEW) proposed a
which-way scheme that, they claimed, entailed no momentum transfer. Storey,
Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed,
showed that Bohr was right. This work reviews and extends a recent proposal
[Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a
weak-valued probability distribution for momentum transfer, P_wv(\wp). We show
that P_wv(\wp) must be wider than h/6s. However, its moments can still be zero
because P_wv(\wp) is not necessarily positive definite. Nevertheless, it is
measurable in a way understandable to a classical physicist. We introduce a new
measure of spread for P_wv(\wp): half of the unit-confidence interval, and
conjecture that it is never less than h/4s. For an idealized example with
infinitely narrow slits, the moments of P_wv(\wp) and of the momentum
distributions are undefined unless a process of apodization is used. We show
that by considering successively smoother initial wave functions, successively
more moments of both P_wv(\wp) and the momentum distributions become defined.
For this example the moments of P_wv(\wp) are zero, and these are equal to the
changes in the moments of the momentum distribution. We prove that this
relation holds for schemes in which the moments of P_wv(\wp) are non-zero, but
only for the first two moments. We also compare these moments to those of two
other momentum-transfer distributions and \hat{p}_f-\hat{p}_i. We find
agreement between all of these, but again only for the first two moments.Comment: 14 pages, 6 figures, submitted to J. Opt.
Informationally complete measurements and groups representation
Informationally complete measurements on a quantum system allow to estimate
the expectation value of any arbitrary operator by just averaging functions of
the experimental outcomes. We show that such kind of measurements can be
achieved through positive-operator valued measures (POVM's) related to unitary
irreducible representations of a group on the Hilbert space of the system. With
the help of frame theory we provide a constructive way to evaluate the
data-processing function for arbitrary operators.Comment: 9 pages, no figures, IOP style. Some new references adde
Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
The Barut-Girardello coherent states (BG CS) representation is extended to
the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson
realizations. The sp(N,R) BG CS take the form of multimode ordinary
Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n
canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode
Hilbert space and the relation between the canonical CS and the u(p,q) BG-type
CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and
their discrete superpositions contain many states studied in quantum optics
(even and odd N-mode CS, pair CS) and provide an approach to quadrature
squeezing, alternative to that of intelligent states. New subsets of weakly and
strongly nonclassical states are pointed out and their statistical properties
(first- and second-order squeezing, photon number distributions) are discussed.
For specific values of the angle parameters and small amplitude of the
canonical CS components these states approaches multimode Fock states with one,
two or three bosons/photons. It is shown that eigenstates of a squared
non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of
the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some
formulas. To appear in J. Phys. A, v. 3
Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedIn quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrodinger equation can be mapped to solutions of the Schrodinger equation for harmonic potentials, both the trapping oscillator and the inverted `oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environmentPeer reviewe
Engineering arbitrary motional ionic state through realistic intensity-fluctuating laser pulses
We present a reliable scheme for engineering arbitrary motional ionic states
through an adaptation of the projection synthesis technique for trapped-ion
phenomena. Starting from a prepared coherent motional state, the Wigner
function of the desired state is thus sculpted from a Gaussian distribution.
The engineering process has also been developed to take into account the errors
arising from intensity fluctuations in the exciting-laser pulses required for
manipulating the electronic and vibrational states of the trapped ion. To this
end, a recently developed phenomenological-operator approach that allows for
the influence of noise will be applied. This approach furnishes a
straightforward technique to estimate the fidelity of the prepared state in the
presence of errors, precluding the usual extensive ab initio calculations. The
results obtained here by the phenomenological approach, to account for the
effects of noise in our engineering scheme, can be directly applied to any
other process involving trapped-ion phenomena.Comment: more information at http://www.df.ufscar.br/~quantum
Motional effects of single trapped atomic/ionic qubit
We investigate theoretical decoherence effects of the motional degrees of
freedom of a single trapped atomic/ionic electronically coded qubit. For single
bit rotations from a resonant running wave laser field excitation, we found the
achievable fidelity to be determined by a single parameter characterized by the
motional states. Our quantitative results provide a useful realistic view for
current experimental efforts in quantum information and computing.Comment: 3 fig
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