Rydberg Population Research Articles

Duality and bistability in an optomechanical cavity coupled to a Rydberg superatom

We study the steady-state behaviors of a typical optomechanical cavity coupled to cold Rydberg atoms with dipole-dipole interactions. The interacting atoms are described as one superatom of three collective states in a ladder configuration in the limit of a strong dipole blockade and a weak cavity field. We find that this hybrid system exhibits phenomena of conditional duality and nonlinear bistability in terms of mirror displacement, number of cavity photons, and Rydberg population, depending on the detuning of the cavity field, the strength of the optical driving field, and the number of cold atoms. It is of particular interest that the two branches of relevant curves may intersect to yield a nontrivial duality and bistability. Such correlated optical, mechanical, and atomic responses arise from the efficient feedback between atom-light and optomechanical interactions and have realistic applications, e.g., in realizing accurate optomechanical detection or attaining deterministic single photons.

Dissipation-sensitive multiphoton excitations of strongly interacting Rydberg atoms

We theoretically investigate the effect of dissipation on multiphoton excitation of Rydberg atoms. The steady states and the dynamics are compared via two types of four-level excitation schemes with different dissipative paths of spontaneous emission. We find that in the case of strong Rydberg-Rydberg interaction, the schemes will settle in several different nonequilibrium steady states. The interesting aspect is that there exist the multistable steady states, which reveals the competition between interaction-induced nonlinearity and dissipation caused by spontaneous emission. A numerical simulation on the Rydberg population dynamics in the bistable region exhibits different features existing in the two schemes even with the same initial conditions, which accounts for the influence of the dissipation on the dynamics.

Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems

We study the impact of dephasing on the excitation dynamics of a cloud of ultracold two-level Rydberg atoms for both resonant and off-resonant laser excitation, using the wave function Monte Carlo (MCWF) technique. We find that while for resonant laser driving, dephasing mainly leads to an increase of the Rydberg population and a decrease of the Mandel Q parameter, at off-resonant driving strong dephasing toggles between direct excitation of pairs of atoms and subsequent excitation of single atoms, respectively. These two excitation mechanisms can be directly quantified via the pair correlation function, which shows strong suppression of the two-photon resonance peak for strong dephasing. Consequently, qualitatively different dynamics arise in the excitation statistics for weak and strong dephasing in off-resonant excitation. Our findings show that time-resolved excitation number measurements can serve as a powerful tool to identify the dominating process in the system's excitation dynamics.

Electrical readout for coherent phenomena involving Rydberg atoms in thermal vapor cells.

We present a very sensitive and scalable method to measure the population of highly excited Rydberg states in a thermal vapor cell of rubidium atoms. We detect the Rydberg ionization current in a 5 mm electrically contacted cell. The measured current is found to be in qualitatively good agreement with a theory for the Rydberg population based on a master equation for the three-level problem, including an ionization channel and the full Doppler distributions at the corresponding temperatures. The signal-to-noise ratio of the current detection is substantially better than that of purely optical techniques.

Collective Quantum Jumps of Rydberg Atoms

We study an open quantum system of atoms with a long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps are inherently collective, and in fact, exist only for a large number of atoms. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden.

Shedding new light on the role of the Rydberg state in the photochemistry of aniline

Efficient electronic relaxation following the absorption of ultraviolet light is crucial for the photostability of biological chromophores, so understanding the microscopic details of the decay pathways is of considerable interest. Here, we employ femtosecond time-resolved photoelectron imaging to investigate the ultrafast intramolecular dynamics of aniline, a prototypical aromatic amine, following excitation just below the second absorption maximum. We find that both the second ππ* state and the Rydberg state are populated during the excitation process. Surprisingly, the dominant non-radiative decay pathway is an ultrafast relaxation mechanism that transfers population straight back to the electronic ground-state. The vibrational energy resolution and photoelectron angular distributions obtained in our experiments reveal an interesting bifurcation of the Rydberg population to two non-radiative decay channels. The existence of these competing non-radiative relaxation channels in aniline illustrates how its photostability arises from a subtle balance between dynamics on different electronically excited states and importantly between Rydberg and valence states.

Antiferromagnetic phase transition in a nonequilibrium lattice of Rydberg atoms

We study a driven-dissipative system of atoms in the presence of laser excitation to a Rydberg state and spontaneous emission. The atoms interact via the blockade effect, whereby an atom in the Rydberg state shifts the Rydberg level of neighboring atoms. We use mean-field theory to study how the Rydberg population varies in space. As the laser frequency changes, there is a continuous transition between the uniform and antiferromagnetic phases. The nonequilibrium nature also leads to a novel oscillatory phase and bistability between the uniform and antiferromagnetic phases.

Dynamics of low-density ultracold Rydberg gases

Population dynamics in weakly excited clouds of ultracold $^{87}\text{R}\text{b}$ Rydberg atoms were studied by means of trap loss, fluorescence detection, and state-dependent stimulated emission. Rydberg atoms were excited to various $nl$ Rydberg states via continuous two-photon excitation from a magneto-optical trap. A stimulated emission probe laser was then used to bring the Rydberg atoms down to the $6{P}_{3/2}$ state, allowing state-dependent detection of the Rydberg atoms. Measurements of trap loss and fluorescent emission reveal information about the evolution of the Rydberg populations. In particular, population in the initial Rydberg state quickly transfers to other Rydberg states by a noncollisional mechanism, likely superradiant emission. The trap-loss measurements are consistent with black-body ionization as the dominant loss mechanism.

Ionization and plasma formation in high n cold Rydberg samples

The experiments reported here show that the dipole-dipole interaction, the fundamental interaction between the cold Rydberg atoms, is the dominant initial ionization mechanism for evolution from a frozen Rydberg gas into a plasma. The study also indicates that plasma formation follows a path of initial ionization, redistribution of Rydberg population to higher angular momentum states, and rapid avalanche ionization due to electron-Rydberg collisions.

Two-color pump-probe study and internal-energy dependence of Rydberg-state excitation inC60

Excitation of Rydberg states in isolated ${\mathrm{C}}_{60}$ is studied by time-resolved photoelectron spectroscopy in a femtosecond two-color pump-probe experiment. The relaxation time for electron-electron interaction is determined to be approximately $100\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ with the ${t}_{1g}(\mathrm{LUMO}+1)$ orbital being considered to define the doorway state in a nonadiabatic multielectron excitation process. The internal energy stored in vibrational modes of the ${\mathrm{C}}_{60}$ at $770\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is found to support the excitation process very efficiently while in ``cold'' ${\mathrm{C}}_{60}$ $(80\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, no significant Rydberg population is detected.

Redistributing populations of Rydberg atoms with half-cycle pulses

Expanding the wave function in terms of eigenstates, we calculated the population redistribution of high-Rydberg hydrogen atoms under the interactions of external time-dependent electromagnetic fields. Our numerical results show that populations of Rydberg atoms can be driven down to lower $n$ levels with a train of half-cycle pulses. Oscillations of the Rydberg population through both $n$ levels and $l$ levels are observed during these interactions. The approach may have applications in providing an effective mechanism for producing near ground-state atoms from the initially high-Rydberg distributions found in recombining ultracold plasmas such as encountered in the antihydrogen trapping experiments at CERN.

Optical control of the rotational angular momentum of a molecular Rydberg wave packet.

An intuitive scheme for controlling the rotational quantum state of a Rydberg molecule is demonstrated experimentally. We determine the accumulated phase difference between the various components of a molecular electron wave packet, and then employ a sequence of phase-locked optical pulses to selectively enhance or depopulate specific rotational states. The angular momentum composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multipulse response of the time-dependent Rydberg populations.

The role of phase in molecular Rydberg wave packet dynamics

The dynamics of Rydberg wave packets in NO are investigated in the regime where the electronic period is comparable with the rotational motion of the molecular ion core. The presence of a rotating molecular core manifests itself in the wave packet dynamics as a series of peaks separated by the rotational beat period TRot, but offset by ΔμTRot, where Δμ is the difference in quantum defect between the two dominant Rydberg series in the superposition. We rationalize this by treating the dynamics of a wave packet created from a coherent superposition of two interleaved Rydberg series as two separate electron wave packets, which interfere with one another when they overlap spatially. There is a periodic phase difference between the two wave packets that depends on the rotational energy of the core in each Rydberg series and also on the quantum defects. The resulting interference pattern in the Rydberg population manifests itself as peaks in the wave packet spectrum at the stroboscopic period.

Ultrafast [2 + 2]-cycloaddition in norbornadiene.

Excitation of norbornadiene (bicyclo[2.2.1]hepta-2,5-diene) at 200 nm populates two states in parallel, the second pi(pi*) state and a Rydberg state. We monitored both populations by transient nonresonant ionization. From the pi(pi*) state the molecule relaxes in consecutive steps with time constants 5, 31 and 55 fs down to the ground-state surface, whereas the Rydberg population merges to the other path on the pi(pi*) surface within 420 fs. The relaxation steps are discussed in terms of conical intersections (CoIns) between different surfaces Information on them is inferred from known spectroscopy and, for the last CoIn, from published calculations on Dewar benzene-->prismane conversion and on ethylene photodimerization for which norbornadiene with its two nonconjugated double bonds is a model. The calculation predicts symmetry breaking for this CoIn, the two ethylenes forming a rhombus Although this distortion is hindered in norbornadiene by ring strain, this CoIn seems easily accessible as indicated by the short time (<55 fs) found for passing through it.

Electric field ionization of high Rydberg states of Ar with sequences of identical pulses.

Novel field-ionization behavior of very high Rydberg states of Ar ( $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}50--250$) is observed using sequential pulsed electric fields. Fast autoionization acts as a filter against adiabatic field ionization near the ${}^{2}{P}_{1/2}$ threshold, whereas both diabatic and adiabatic field ionization occur near the ${}^{2}{P}_{3/2}$ threshold. Sequences of up to 9 equivalent pulses yield recurrent field ionization signals near the ${}^{2}{P}_{3/2}$ threshold, provided that the field returns close to zero between pulses, demonstrating a statistical redistribution of the Rydberg population amongst all states of a given Stark manifold near zero field.

Rotational autoionization dynamics in high Rydberg states of nitrogen

The decay dynamics of the high Rydberg states of N2 converging on the first few rotational levels (N+=0,1,2,3) of the ground vibronic X 2Σ+g (v+=0) state of the N+2 cation have been investigated by delayed pulsed field ionization (PFI) following two-photon enhanced (2+1′) three-photon excitation via the a″ 1Σ+g (v′=0) state of N2. The experiments were carried out in the presence of a weak homogeneous dc electric field and at typical ion densities of 200–2000 ions/mm3. All Rydberg states in the range of principal quantum number n=140–200 exhibit extreme stability against autoionization and predissociation and some have lifetimes which exceed 30 μs. The decay of the highest Rydberg states beyond n=200 is induced by external perturbations (field ionization and collisional ionization) and no Rydberg states beyond n=350 can be observed by delayed PFI. The Rydberg states which converge on the N+=0 and 1 rotational levels of the ion, and which therefore are not subject to rotational autoionization, decay into neutral products (by a process presumed to be predissociation) in less than 7 μs in the range n&amp;lt;100. The importance of predissociation is greatly reduced beyond n=100 and becomes negligible on our experimental timescale (30 μs) above n=140. The decay of the Rydberg states converging on the N+=2 and 3 rotational levels of the ion is more complex. Below n=100, only 30%–40% of the Rydberg population decays by fast rotational autoionization whereas 60%–70% decays by predissociation. The importance of predissociation decreases rapidly above n=100 and becomes negligible beyond n=140. The decay by rotational autoionization can be observed at all n values but becomes noticeably slower beyond n=100. In the range n=140–200 it exhibits a marked biexponential decaying behavior with 30% of the population decaying within a few microseconds and 70% displaying long term stability (τ≳30 μs). The branching between predissociation and autoionization is explained by the effect of the dc electric field which mixes strongly the optically accessible p Rydberg series with the high l manifold beyond n=100. The long lifetimes observed experimentally indicate that ml mixing becomes important as soon as l mixing sets in.

Studies of high charge state Rydberg ions

High charge state Rydberg ions formed through charge capture are being studied using a novel Rydberg analyzer. The analyser, following the design of MacAdam and Rolfes [K.B. MacAdam and R.G. Rolfes, Rev. Sci. Instr. 53 (1982) 592], uses electric field ionization to give P( n), the population of the level characterized by principal quantum number n, differentially in n. However, it differs significantly from the MacAdam device in that: (1) electrons, not ions, are energy analyzed; (2) electron energies are measured at 0° with respect to the ion beam axis; and (3) because of (1) and (2) the analyzer is capable of evaluating Rydberg populations even in high charge state, high energy ions. As an example, we have examined the Rydberg states created in collisions of 0.5 MeV/amu highly charged fluorine with neon. Data and some operating modes of the device will be presented.

Electric field ionization of highly excited sodiumndatoms

Selective field ionization (SFI) is frequently used to detect atoms in high Rydberg states and to analyze Rydberg population distributions. In order to realize the full potential of this technique, however, a detailed understanding of the behavior of Rydberg atoms during passage from low to ionizing fields is required. The factors influencing this passage are discussed quantitatively and are illustrated by means of detailed SFI data obtained for $\mathrm{Na}34d$ atoms.

Investigation of nonadiabatic effects in molecular-hydrogen Rydberg states by electric field ionization

The technique of electric field ionization has been used to study molecular Rydberg states of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ formed by electron capture of ${\mathrm{H}}_{2}^{+}$ or ${\mathrm{D}}_{2}^{+}$ beams in ${\mathrm{H}}_{2}$. The neutral molecules were passed through two intense electric field ionization regions in tandem, separated by an \ensuremath{\sim} ${10}^{\ensuremath{-}7}$-sec drift region. Up to 15% of the Rydberg population removed by the first ionization region was repopulated during transit through the drift region. This result has been interpreted in terms of nonadiabatic state mixing of nearly degenerate adiabatic molecular states. A difference in the state repopulation between Rydberg states of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ was observed, indicating the importance of the rovibrational spectrum on the repopulation mechanism. By comparison, similar studies on atomic Rydberg states showed no difference between H and D. Moreover, the atoms exhibited only a small repopulation effect, consistent with the contribution due to $\stackrel{\ensuremath{\rightarrow}}{1}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$ coupling.