Long-Range Tails in van der Waals Interactions of Excited-State and Ground-State Atoms

A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term, and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded 1/R^7 Casimir-Polder form to a long-range tail-provided by the Wick-rotated term-proportional to cos[2 (E_m-E_n) R/(hbar c)]/R^2, where E_m < E_n is the energy of a virtual state, lower than the reference state energy E_n, and R is the interatomic separation. General expressions are obtained which can be applied to atomic reference states of arbitrary angular symmetry. Careful treatment of the pole terms in the Feynman prescription for the atomic polarizability is found to be crucial in obtaining correct results.Comment: 13 pages; RevTe

Non-classical properties of the e.m. near field of an atom in spontaneous light emission

We use Glauber's correlation function function as well as the Green functions formalism to investigate, in the case of a dipolar atomic transition, the causal behaviour of the spontaneously emitted electromagnetic field. We also examine the role played by the longitudinal electric field, which is not described in terms of photonic (transverse) degrees of freedom. We predict the existence of a genuinely quantum memory effect at the level of the near field surrounding the atom, which keeps track of the past excitation and emission by the atom

Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n >= 3

The long-range interaction of excited neutral atoms has a number of interesting and surprising properties, such as the prevalence of long-range, oscillatory tails, and the emergence of numerically large can der Waals C_6 coefficients. Furthermore, the energetically quasi-degenerate nP states require special attention and lead to mathematical subtleties. Here, we analyze the interaction of excited hydrogen atoms in nS states (3 <= n <= 12) with ground-state hydrogen atoms, and find that the C_6 coefficients roughly grow with the fourth power of the principal quantum number, and can reach values in excess of 240,000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R << a_0/alpha, where a_0 is the Bohr radius and alpha is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a_0/alpha << R << hbar c/L, where L is the Lamb shift energy. In this range, the contribution of quasi-degenerate excited nP states remains nonretarded and competes with the 1/R^2 and 1/R^4 tails of the pole terms which are generated by lower-lying mP states with 2 <= m <= n-1, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range R >> hbar c/L. The familiar 1/R^7 asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation, for highly excited states.Comment: 17 pages; RevTe

Virtual Resonant Emission and Oscillatory Long-Range Tails in van der Waals Interactions of Excited States: QED Treatment and Applications

We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails which are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term which depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the ungerade state for close approach), and we include all nonresonant states in our rigorous QED treatment. In order to illustrate the findings, we analyze the fine-structure resolved van der Waals interaction for nD-1S hydrogen interactions with n=8,10,12 and find surprisingly large numerical coefficients.Comment: 6 pages; RevTe

Conditions for anti-Zeno effect observation in free-space atomic radiative decay

Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article, Nature 405, 546 (2000), Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of analytical results available for hydrogen-like atoms, we find that in free space, only non-electric-dipolar transitions should present an observable AZE, revealing that this effect is consequently much less ubiquitous than first predicted. We then propose an experimental scheme for AZE observation, involving the electric quadrupole transition between D 5/2 and S 1/2 in the heaviest alkali-earth ions Ca + and Sr +. The proposed protocol is based on the STIRAP technique which acts like a dephasing quasi-measurement

The onset time of Fermi's golden rule

Fermi's golden rule describes the decay dynamics of unstable quantum systems coupled to a reservoir, and predicts a linear decay in time. Although it arises at relatively short times, the Fermi regime does not take hold in the earliest stages of the quantum dynamics. The standard criterion in the literature for the onset time of the Fermi regime is $t_F\sim1/\Delta\omega$, with $\Delta\omega$ the frequency interval around the resonant transition frequency $\omega_0$ of the system, over which the coupling to the reservoir does not vary appreciably. In this work, this criterion is shown to be inappropriate in general for broadband reservoirs, where the reservoir coupling spectrum takes the form $R\left(\omega\right)\propto\omega^\eta$, and for which it is found that for $\eta>1$, the onset time of the Fermi regime is given by $t_F\propto\left(\omega_{\mathrm{X}}/\omega_0\right)^{\eta-1}\times1/\omega_0$ where $\omega_{\mathrm{X}}$ is the high-frequency cutoff of the reservoir. Therefore, the onset of the Fermi regime can take place at times orders of magnitude larger than those predicted by the standard criterion. This phenomenon is shown to be related to the excitation of the off-resonant frequencies of the reservoir at short times. For broadband reservoirs with $\eta\leq1$, and for narrowband reservoirs, it is shown that the standard criterion is correct. Our findings revisit the conditions of applicability of Fermi's golden rule and improve our understanding of the dynamics of unstable quantum systems