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arXiv:2101.03107 · Physical Review A

Blackbody-radiation-noise broadening of quantum systems

Eric B. Norrgard, Stephen Eckel, Christopher L. Holloway, Eric L. Shirley

Published Apr 5, 2021• 2 citations
arXivHTMLPDF

Abstract

Precision measurements of quantum systems often seek to probe or must account for the interaction with blackbody radiation. Over the past several decades, much attention has been given to ac Stark shifts and stimulated state transfer. For a blackbody in thermodynamic equilibrium, these two effects are determined by the expectation value of photon number in each mode of the Planck spectrum. Here we explore how the photon number variance of an equilibrium blackbody generally leads to a parametric broadening of the energy levels of quantum systems that is inversely proportional to the square root of the blackbody volume. We consider the effect in two cases which are potentially highly sensitive to this broadening: Rydberg atoms and atomic clocks. We find that even in blackbody volumes as small as 1 ${\mathrm{cm}}^{3}$, this effect is unlikely to contribute meaningfully to transition linewidths.

DOI
10.1103/physreva.103.042806

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Precision measurements of quantum systems often seek to probe or must account for the interaction with blackbody radiation. Over the past several decades, much attention has been given to ac Stark shifts and stimulated state transfer. For a blackbody in thermodynamic equilibrium, these two effects are determined by the expectation value of photon number in each mode of the Planck spectrum. Here we explore how the photon number variance of an equilibrium blackbody generally leads to a parametric broadening of the energy levels of quantum systems that is inversely proportional to the square root of the blackbody volume. We consider the effect in two cases which are potentially highly sensitive to this broadening: Rydberg atoms and atomic clocks. We find that even in blackbody volumes as small as 1 cm3{\mathrm{cm}}^{3}cm3, this effect is unlikely to contribute meaningfully to transition linewidths.
Transitions between energetically close-lying Rydberg states are characterized by large electric dipole matrix elements and frequencies low enough that at room temperature the photon occupation number is \ensuremath{\simeq} 10. Consequently the absorption of blackbody radiation and the stimulated emission produced by it lead to an efficient redistribution of population among nearby levels. In some cases dramatic effects are observed, for example, radiative lifetimes that are shortened to a small fraction of their T=0T=0T=0 values. In addition, the 300-K blackbody field of \ensuremath{\sim}10 V/cm produces ac Stark shifts of the Rydberg levels. Calculations of the population redistribution effects and ac Stark shifts are presented. Examples are given to illustrate that care must be taken in experiments with highly excited atoms to ensure that only one state is being observed rather than a distribution.
We consider the Zeeman shift in Rydberg atoms induced by room-temperature blackbody radiation (BBR). BBR shifts to the Rydberg levels are dominated by the familiar BBR Stark shift. However, the BBR Stark shift and the BBR Zeeman shift exhibit different behaviors with respect to the principal quantum number of the Rydberg electron. Namely, the BBR Stark shift asymptotically approaches a constant value given by a universal expression, whereas the BBR Zeeman shift grows steeply with principal quantum number due to the diamagnetic contribution. We show that for transitions between Rydberg states, where only the differential shift between levels is of concern, the BBR Zeeman shift can surpass the BBR Stark shift. We exemplify this in the context of a proposed experiment targeting a precise determination of the Rydberg constant.
Blackbody radiation is expected to produce a temperature-dependent Stark shift in atomic Rydberg states. Unfortunately, in "one-electron" atoms, all the Rydberg levels experience the same shift, and the effect is only observable on an optical transition from the ground state. However, in a many-electron atom the presence of valence-state perturbers leads to unequal shifts of the Rydberg levels. This should make it possible to observe the frequency shift of a transition between two neighboring Rydberg states at a frequency in the radio-frequency range. This eliminates the need for a very stable visible laser, which so far has been the major technical obstacle to the observation and utilization of the effect. We present as an example a specific case in Ba.
Abstract First evaluations of the blackbody-radiation (BBR)-induced shift and broadening of highly excited Rydberg states were based on the account of only the first term of the expansion for the Planck’s distribution in powers of the ratio of the BBR-photon energy to the environmental thermal energy. The corresponding asymptotic expression for the shift is proportional to a sum rule for the oscillator strengths, which is identical for all states, independently of their principal and angular-momentum quantum numbers. The broadening appeared proportional to the sum of the oscillator-strength first moments, which is dependent on only the principal quantum number, being independent of the state’s angular momentum. In this article, we demonstrate that the account of higher-order terms of the Planck’s distribution expansion provides corrections revealing the dependence of asymptotic shift and broadening on the Rydberg-state principal and angular-momentum quantum numbers. The strongest corrections are observed for states with low angular momenta, in agreement with earlier performed numerical calculations. Sum rules for higher moments of oscillator strengths are used for evaluating the corrections for the BBR-induced broadening and shift of Rydberg-state energy levels in neutral atoms and ions of arbitrary nuclear charge Z .
A highly excited (Rydberg) atom bathed in blackbody radiation is perturbed in two ways. A dynamic Stark shift is induced by the off-resonant components of the blackbody radiation. Additionally, electric-dipole transitions to other atomic energy levels are induced by the resonant components of the blackbody radiation. This depopulation effect shortens the Rydberg-state lifetime, thereby broadening the energy level. Calculations of these two effects in many states of hydrogen, helium, and the alkali-metal atoms Li, Na, K, Rb, and Cs are presented for T=300T=300T=300 K. Contributions from the entire blackbody spectrum and from both discrete and continuous perturbing states are included. The accuracy is considerably greater than that of previous estimates.
Blackbody radiation affects low-frequency (${h}_{\ensuremath{\nu}}\ensuremath{\ll}\mathrm{kT}$) atomic transitions both by inducing transitions and producing ac frequency shifts, important effects that have previously been ignored. Here we report the calculation and experimental observation of a manifestation of the former, the threefold reduction of the Na np\mathrm{np}np radiative lifetimes by 300-K blackbody-radiation-induced stimulated emission and absorption. Estimates of ac frequency shifts for Rydberg and ground-state atoms are given.