Photoassociation and coherent transient dynamics in the interaction of ultracold rubidium atoms with shaped femtosecond pulses - II. Theory
Andrea Merli, Frauke Eimer, Fabian Weise, Albrecht Lindinger, Wenzel Salzmann, Terry Mullins, Simone Gotz, Roland Wester, Matthias Weidemuller, Ruzin Aganoglu, Christiane P. Koch
Photoassociation of ultracold rubidium atoms with femtosecond laser pulses is studied theoretically. The spectrum of the pulses is cut off in order to suppress pulse amplitude at and close to the atomic resonance frequency. This leads to long tails of the laser pulse as a function of time giving rise to coherent transients in the photoassociation dynamics. They are studied as a function of cutoff position and chirp of the pulse. Molecule formation in the electronically excited state is attributed to off-resonant excitation in the strong-field regime.
We experimentally investigate various processes present in the photoassociative interaction of an ultracold atomic sample with shaped femtosecond laser pulses. We demonstrate the photoassociation of pairs of rubidium atoms into electronically excited, bound molecular states using spectrally cut femtosecond laser pulses tuned below the rubidium D1 or D2 asymptote. Time-resolved pump-probe spectra reveal coherent oscillations of the molecular formation rate, which are due to coherent transient dynamics in the electronic excitation. The oscillation frequency corresponds to the detun-ing of the sp…
An experimental pump-probe study of the photoassociative creation of translationally ultracold rubidium molecules is presented together with numerical simulations of the process. The formation of loosely bound excited-state dimers is observed as a first step towards a fully coherent pump-dump approach to the stabilization of Rb$_2$ into its lowest ground vibrational states. The population that contributes to the pump-probe process is characterized and found to be distinct from a background population of pre-associated molecules.
Photoassociation with short laser pulses has been proposed as a technique to create ultracold ground state molecules. A broad-band excitation seems the natural choice to drive the series of excitation and deexcitation steps required to form a molecule in its vibronic ground state from two scattering atoms. First attempts at femtosecond photoassociation were, however, hampered by the requirement to eliminate the atomic excitation leading to trap depletion. On the other hand, molecular levels very close to the atomic transition are to be excited. The broad bandwidth of a femtosecond laser then a…
Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5P_{1/2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechan…
Two-photon photoassociation of hot magnesium atoms by femtosecond laser pulses, creating electronically excited magnesium dimer molecules, is studied from first principles, combining \textit{ab initio} quantum chemistry and molecular quantum dynamics. This theoretical framework allows for rationalizing the generation of molecular rovibrational coherence from thermally hot atoms [L. Rybak \textit{et al.}, Phys. Rev. Lett. {\bf 107}, 273001 (2011)]. Random phase thermal wave functions are employed to model the thermal ensemble of hot colliding atoms. Comparing two different choices of basis func…
The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalize…
Quantum coherent control of ultrafast bond making and the subsequent molecular dynamics is crucial for the realization of a new photochemistry, where a shaped laser field is actively driving the chemical system in a coherent way from the thermal initial state of the reactants to the final state of the desired products. We demonstrate here coherent control over the relative yields of Mg$_2$ molecules that are generated via photoassociation and subsequently photodriven into different groups of final states. The strong-field process involves non-resonant multiphoton femtosecond photoassociation o…
The potential energy curves, permanent and transition dipole moments, and the static dipolar polarizability, of molecular ions composed of one alkali-metal atom and a Strontium ion are determined with a quantum chemistry approach. The molecular ions are treated as effective two-electron systems and are treated using effective core potentials including core polarization, large gaussian basis sets, and full configuration interaction. In the perspective of upcoming experiments aiming at merging cold atom and cold ion traps, possible paths for radiative charge exchange, photoassociation of a cold …
We explore long-range interactions between two atoms excited into high principal quantum number n Rydberg states, and present calculated potential energy surfaces (PES) for various symmetries of doubly excited ns and np rubidium atoms. We show that the PES for these symmetries exhibit deep (~GHz) potential wells, which can support very extended (~micrometers) bound vibrational states (macrodimers). We present n-scaling relations for both the depth De of the wells and the equilibrium separations Re of these macrodimers, and explore their response to small electric fields and stability with resp…
We report on the combined action of a cw diode laser and a train of ultrashort pulses when each of them drives one step of the 5S-5P-5D two-photon transition in rubidium vapor. The fluorescence from the 6P_{3/2} state is detected for a fixed repetition rate of the femtosecond laser while the cw-laser frequency is scanned over the rubidium D_{2} lines. This scheme allows for a velocity selective spectroscopy in a large spectral range including the 5D_{3/2} and 5D_{5/2} states. The results are well described in a simplified frequency domain picture, considering the interaction of each velocity g…
Utilizing single-photon photoassociation, we have achieved ultracold rubidium molecules with a high number density that provides a new efficient approach toward molecular quantum degeneracy. A new detection mechanism for ultracold molecule utilizing the inelastic atom-molecule collision is demonstrated. The resonant coupling effect on the formation of the ${\rm X^1Σ^+_g}$ ground state ${\rm ^{85}Rb_2}$ allows for a sufficient number of more deeply bound ultracold molecules, which induced an additional trap loss and heating of the co-existing atoms owing to the inelastic atom-molecule collision…
The first step in the coherent control of a photoinduced binary reaction is bond making or photoassociation. We have recently demonstrated coherent control of bond making in multi-photon femtosecond photoassociation of hot magnesium atoms, using linearly chirped pulses [Levin et al., arXiv:1411.1542]. The detected yield of photoassociated magnesium dimers was enhanced by positively chirped pulses which is explained theoretically by a combination of purification and chirp-dependent Raman transitions. The yield could be further enhanced by pulse optimization resulting in pulses with an effective…
An experimental realization of high-precision direct frequency comb spectroscopy using counter-propagating femtosecond pulses on two-photon atomic transitions is presented. Doppler broadened background signal, hampering precision spectroscopy with ultrashort pulses, is effectively eliminated with a simple pulse shaping method. As a result, all four 5S-7S two-photon transitions in a rubidium vapor are determined with both statistical and systematic uncertainties below 10$^{-11}$, which is an order of magnitude better than previous experiments on these transitions.
We report on coherent control of excitation processes of translationally ultracold rubidium dimers in a magneto-optical trap by using shaped femtosecond laser pulses. Evolution strategies are applied in a feedback loop in order to optimize the photoexcitation of the Rb2 molecules, which subsequently undergo ionization or fragmentation. A superior performance of the resulting pulses compared to unshaped pulses of the same pulse energy is obtained by distributing the energy among specific spectral components. The demonstration of coherent control to ultracold ensembles opens a path to actively i…
We investigate the dynamics of molecular photoexcitation by unchirped femtosecond laser pulses using RbCs as a model system. This study is motivated by a goal of optimizing a two-color scheme of transferring vibrationally-excited ultracold molecules to their absolute ground state. In this scheme the molecules are initially produced by photoassociation or magnetoassociation in bound vibrational levels close to the first dissociation threshold. We analyze here the first step of the two-color path as a function of pulse intensity from the low-field to the high-field regime. We use two different a…
We demonstrate subpicosecond-time-scale population transfer between the pair of hyperfine ground states of atomic rubidium using a single laser-pulse. Our scheme utilizes the geometric and dynamic phases induced during Rabi oscillation through the fine-structure excited state in order to construct an $X$ rotation gate for the hyperfine-state qubit system. Experiment performed with a femtosecond laser and cold rubidium atoms, in a magneto-optical trap, shows over 98\% maximal population transfer between the clock states.
We report the investigation of a collimated blue light generated in rubidium vapor due to the combined action of an ultrashort pulse train and a cw diode laser. Each step of the two-photon transition 5S - 5P$_{3/2}$ - 5D is excited by one of the lasers, and the induced coherence between the 5S and 6P$_{3/2}$ states is responsible for generating the blue beam. Measurements of the excitation spectrum reveal the frequency comb structure, indicating that each individual mode is responsible for inducing a nonlinear process. The strong signal dependency on the atomic density is characterized by a sh…
We investigate the interaction between two rubidium atoms in highly excited Rydberg states, and find that very long-range potential wells exist. These wells are shown to support many bound states. We calculate the properties of the wells and bound levels, and show that their lifetimes are limited by that of the constituent Rydberg atoms. We also show how these $μ$m-size bound states can be populated {\it via} photoassociation (PA), and how the signature of the ad-mixing of various $\ell$-character producing the potential wells could be probed. We discuss how sharp variations of the PA rate %to…
We have performed high resolution photoassociation spectroscopy of rubidium ultra long-range Rydberg molecules in the vicinity of the 25$P$ state. Due to the hyperfine interaction in the ground state perturber atom, the emerging mixed singlet-triplet potentials contain contributions from both hyperfine states. We show that this can be used to induce remote spin-flips in the perturber atom upon excitation of a Rydberg molecule. When furthermore the spin-orbit splitting of the Rydberg state is comparable to the hyperfine splitting in the ground state, the orbital angular momentum of the Rydberg …
We present the principle and experimental demonstration of Time Resolved Quantum State Holography. The quantum state of an excited state interacting with an ultrashort chirped laser pulse is measured during this interaction. This has been obtained by manipulating coherent transients created by the interaction of femtosecond shaped pulses and rubidium atoms.
We propose and demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The effect is demonstrated experimentally by observing piecewise excitation of Rubidium atoms from 5s_1/2 to 5p_…
We demonstrate for the first time coherent control of bond making, a milestone on the way to coherent control of photo-induced bimolecular chemical reactions. In strong-field multiphoton femtosecond photoassociation experiments, we find the yield of detected magnesium dimer molecules to be enhanced for positively chirped pulses and suppressed for negatively chirped pulses. Our ab initio model shows that control is achieved by purification via Franck-Condon filtering combined with chirp-dependent Raman transitions. Experimental closed-loop phase optimization using a learning algorithm yields an…
The methods producing cold molecules from cold atoms tend to leave molecular ensembles with substantial residual internal energy. For instance, Cs2 molecules initially formed via photoassociation of cold Cs atoms are in several vibrational levels, v, of the electronic ground state. Here we apply a broadband femtosecond laser that redistributes the vibrational population in the ground state via a few electronic excitation - spontaneous emission cycles. The laser pulses are shaped to remove the excitation frequency band of the v = 0 level, preventing re-excitation from that state. We observe a f…
We investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85Rb2 molecules in a magneto-optical trap. We find for optimized pulse shapes an improvement for the formation of ground state molecules by more than a factor of 10 compared to unshaped pulses at the same pump-dump delay time, and by 40% compared to uns…
Arbitrary rotation of a qubit can be performed with a three-pulse sequence; for example, ZYZ rotations. However, this requires precise control of the relative phase and timing between the pulses, making it technically challenging in optical implementation in a short time scale. Here we show any ZYZ rotations can be implemented with a single laser-pulse, that is {\it a chirped pulse with a temporal hole}. The hole of this shaped pulse induces a non-adiabatic interaction in the middle of the adiabatic evolution of the chirped pulse, converting the central part of an otherwise simple Z-rotation t…
We experimentally demonstrate two-photon absorption (TPA) with broadband down-converted light (squeezed vacuum). Although incoherent and exhibiting the statistics of a thermal noise, broadband down-converted light can induce TPA with the same sharp temporal behavior as femtosecond pulses, while exhibiting the high spectral resolution of the narrowband pump laser. Using pulse-shaping methods, we coherently control TPA in Rubidium, demonstrating spectral and temporal resolutions that are 3-5 orders of magnitude below the actual bandwidth and temporal duration of the light itself. Such properties…
We report the preparation of a 780.2 nm and 852.3 nm laser device based on single-pass periodically poled magnesium-oxide-doped lithium niobate (PPMgO:LN) bulk crystals and diode-laser-seeded fiber amplifiers. First, a single-frequency continuously tunable 780.2 nm laser of more than 600 mW from second-harmonic generation (SHG) by a 1560.5 nm laser can be achieved. Then, a 250 mW light at 852.3 nm is generated and achieves an overall conversion efficiency of 4.1% from sum-frequency generation (SFG) by mixing the 1560.5 nm and 1878.0 nm lasers. The continuously tunable range of 780.2 nm and 852…
We report an experimental demonstration of optical 2DCS in cold atoms. The experiment integrates a collinear 2DCS setup with a magneto-optical trap (MOT), in which cold rubidium (Rb) atoms are prepared at a temperature of about 200 $μ$K and a number density of $10^{10}$ cm$^{-3}$. With a sequence of femtosecond laser pulses, we first obtained one-dimensional second- and fourth-order nonlinear signals and then acquired both one-quantum and zero-quantum 2D spectra of cold Rb atoms. The capability of performing optical 2DCS in cold atoms is an important step toward optical 2DCS study of many-body…
It is well known that area pulses make Rabi oscillation and chirped pulses in the adiabatic interaction regime induce complete population inversion of a two-state system. Here we show that chirped zero-area pulses could engineer an interplay between the adiabatic evolution and Rabi-like oscillations. In a proof-of-principle experiment utilizing spectral chirping of femtosecond laser pulses with a resonant spectral hole, we demonstrate that the chirped zero-area pulses could induce, for example, complete population inversion and return of the cold rubidium atom two-state system. Experimental re…
An unexpected interference effect between four-wave mixing excitation routes in rubidium vapor is observed using a combination of a cw diode laser and a 1 GHz femtosecond pulse train. The generated coherent blue light is analyzed by scanning the diode frequency and the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler-Townes splitting and a large separation is observed in the doublet structure due to the configuration of copropagating fields. Remarkably, by scanning the repetition rate, a narrow peak appears as a signature of the interfering pathways. A non-p…
The chirped-pulse interaction in the adiabatic coupling regime induces cyclic permutations of the energy states of a three-level system in the $V$-type configuration, which process is known as the three-level chirped rapid adiabatic passage. Here we show that a spectral hole in a chirped pulse can turn on and off one of the two adiabatic crossing points of this process, reducing the system to an effective two-level system. The given hybrid adiabatic-nonadiabatic transition results in selective excitation of the three-level system, controlled by the laser intensity and spectral position of the …
