Direct single-shot observation of millimeter-wave superradiance in Rydberg-Rydberg transitions

Abstract

We have directly detected millimeter wave (mm-wave) free space superradiant emission from Rydberg states (n ∼ 30) of barium atoms in a single shot. We trigger the cooperative effects with a weak initial pulse and detect with single-shot sensitivity and 20 ps time resolution, which allows measurement and shot-by-shot analysis of the distribution of decay rates, time delays, and timedependent frequency shifts. Cooperative line shifts and decay rates are observed that exceed values that would correspond to the Doppler width of 250 kHz by a factor of 20 and the spontaneous emission rate of 50 Hz by a factor of 10 5 . The initial superradiant output pulse is followed by evolution of the radiation-coupled many-body system toward complex long-lasting emission modes. A comparison to a mean-field theory is presented which reproduces the quantitative time-domain results, but fails to account for either the frequency-domain observations or the long-lived features.Superradiance is an effect in which emitters radiate collectively and coherently due to constructive interference between electric dipoles that communicate with each other via a shared radiation field [1]. Subradiance is exactly the opposite -a collective inhibition of radiation due to destructive interference between the radiation from an array of dipoles [2,3]. These cooperative phenomena provide insights into fundamental many-body physics [4][5][6] and suggest applications ranging from quantum information storage [7][8][9] to narrow linewidth lasers [10][11][12][13].The large electric dipole transition moments and long wavelengths associated with Rydberg-Rydberg transitions make these transitions natural candidates for observing collective effects at relatively low atom number densities (ρ ∼ 10 6 cm −3 ). Hydrogenic scaling rules show that, for ∆n = 1 (where n is the principal quantum number), the transition dipole moment between Rydberg states scales as µ ∝ n 2 and the wavelength scales as λ ∝ n 3 . The transition dipole moment controls only the individual atom spontaneous decay rate, which is independent of density. Collective effects, however, scale in multiples of the spontaneous decay rate. The multiplicative factors scale as the optical depth (OD = ρλ 2 L, where ρ is the density and L is the length of the sample) [6] or the relative density (RD = ρλ 3 ) [14]. Thus, these two scaling rules result in strong collective effects at several orders of magnitude lower densities than between valence states of atoms or molecules. Superradiant emission is also focused primarily on the transition with the smallest ∆n allowed by the ∆ = ±1 angular momentum selection rule [15]. For Rydberg states with n ∼ 30, ∆n = 1 transitions lie at ∼300 GHz (λ ∼ 1mm) and have transition moments on the order of 500 debye [16].Typically, the total number of Rydberg state atoms in a single experiment has been too small to permit direct detection of the emitted electric field. Previous studies of collective effects in ensembles of Rydberg states have relied on state-selective field ioni...

Coherent laser-millimeter-wave interactions en route to coherent population transfer

“…2, summarized here. 2,[40][41][42][43] Barium atoms are generated by ablation of a barium target with a ≤50 mJ pulse of the 1064 nm fundamental of a Nd:YAG laser, focused to a ∼1 mm 2 spot size. We allow the Q-switch to remain open after the initial laser pulse, which causes postablation localized melting of the Ba target.…”

Laser driven superradiant ensembles of two-level atoms near Dicke's regime

“…In 1954, Dicke predicted that the radiation emitted by a dense ensemble of atoms should be dramatically different than the emission from independent atoms [1]. According to Dicke, the decay of a fully inverted cloud of N emitters confined in a region smaller than their transition wavelength is characterized by a burst of radiation with peak intensity scaling ∝ N 2 , rather than the expected ∝ N. This behavior, known as superradiance (or superfluorescence), has been investigated in many experimental platforms including low density clouds of atoms or molecules [2][3][4][5][6][7][8], semiconductors [9,10], nuclei [11], superconducting qubits [12] and Rydberg gases [13][14][15][16]. Recently, interest in superradiance has grown, following theoretical proposals [17,18] and experiments [19][20][21][22][23][24] that describe how superradiance could help realize a novel class of ultra-stable lasers.…”

Superradiance and subradiance in inverted atomic arrays

“…1(a). This phenomenon has been experimentally observed in a wide variety of systems, ranging from thermal gases [4][5][6] to Bose-Einstein condensates [7,8] and Rydbeg atoms [9][10][11].…”