Rydberg spectrum of a single trapped 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>Ca</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math>
 ion: A Floquet analysis

Pawlak, Mariusz; Sadeghpour, H. R.

doi:10.1103/physreva.101.052510

Cited by 8 publications

(3 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work we are interested in the entropic properties of the highly and very highly excited (Rydberg) states (recently shown to be experimentally accessible (see e.g. [51][52][53][54][55][56]) and proved to be very useful for quantum technologies [35,36]) where these properties are most difficult to compute because they possess large and very large values of the principal hyperquantum number n [57,58]. Since the dependence on n for the Rényi entropies is concentrated in their radial part according to equations ( 19)-( 21), the calculation of R q [γ n,l,{μ} ] for the D-dimensional hydrogenic Rydberg states reduces to determine the value of the radial Rényi entropy R q [M n,l ], given by equation (24), in the limiting case n → ∞.…”

Section: Hydrogenic R éNyi Entropy In Momentum Spacementioning

confidence: 99%

“…For instance, when h(x) and F(x) are the Jacobi weights, using the machinery developed in [38] we can check validity of (56) under condition (42). Moreover, we can evaluate the explicit expression of the limiting integral in (56) and can get the rate of growth Ī(q) n when ( 42) is not fulfilled. Then, the following result follows in a straightforward manner.…”

Section: Q -Asymptotics Of Orthonormal Polynomials: General and Jacob...mentioning

confidence: 99%

See 1 more Smart Citation

Rydberg multidimensional states: Rényi and Shannon entropies in momentum space

Aptekarev¹,

Belega²,

Dehesa³

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Rydberg) states is quantified by means of the Rényi and Shannon entropies of its momentum probability density. These quantities, which rest at the core of numerous fields from atomic and molecular physics to quantum technologies, are determined by means of a methodology based on the strong degree-asymptotics of a modified L q -norm of the Gegenbauer polynomials which control the wavefunctions of these states in momentum space. The leading term of these entropic quantities is found from first principles, i.e. by means of the Coulomb potential parameters (space dimensionality, the nuclear charge) and the states’s hyperquantum numbers, in a rigorous simple manner. It is shown that they fulfill a logarithmic growth scaling law with the principal hyperquantum number n which characterizes the Rydberg state.

show abstract

Section: Hydrogenic R éNyi Entropy In Momentum Spacementioning

confidence: 99%

Section: Q -Asymptotics Of Orthonormal Polynomials: General and Jacob...mentioning

confidence: 99%

Rydberg multidimensional states: Rényi and Shannon entropies in momentum space

Aptekarev¹,

Belega²,

Dehesa³

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Nowadays there exists an increasing interest for multidimensional harmonic oscillators from neural networks [16], fractional and quantum statistics [17,18,19,20,21], classical and quantum information [22,23,24,25,26,27,28,29,30], high-energy physics [15,31] to quantum chemistry and atomic and molecular physics [6,32,33,34,35,36,37].…”

Section: Introductionmentioning

confidence: 99%

Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators

Dehesa

Toranzo

2020

Preprint

View full text Add to dashboard Cite

The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like quantities (Fisher information, Shannon and Rényi entropies, disequilibrium) of its quantum probability distribution together with their associated uncertainty relations. They are explicitly given, at times in a closed compact form, by means of the potential parameters (oscillator strength, dimensionality, D) and the hyperquantum numbers (nr, µ1, µ2, . . . , µD−1) which characterize the state. Emphasis is placed on the highly-excited Rydberg (high radial hyperquantum number nr, fixed D) and the high-dimensional (high D, fixed hyperquantum numbers) states. We have used a methodology where the theoretical determination of the integral functionals of the Laguerre and Gegenbauer polynomials, which describe the spreading quantities, leans heavily on the algebraic properties and asymptotical behavior of some weighted Lq-norms of these orthogonal functions.

show abstract