Rydberg spectroscopy of rubidium cold atoms trapped in a magneto-optical trap (MOT) was performed in a quartz cell. When electric fields acting on the atoms generated by a plate external to the cell were continuously applied, electric charges on the cell walls were created, as monitored on the Rydberg spectra. Avoiding accumulation of the charges and realizing good control over the applied electric field was instead obtained when the fields were applied only for a short time, typically a few microseconds. In a two-photon excitation via the 62P state to the Rydberg state, the laser resonant with the 52S–62P transition photoionizes the excited state. The photoionization-created ions produce an internal electric field which deforms the excitation spectra, as monitored on the Autler-Townes absorption spectra.
© 2011 Optical Society of America
In recent years, Rydberg atoms have been the subject of intense study  and have become an important tool for several branches of quantum physics such as quantum-information processing with neutral atoms [2–4], production of single-atom as well as single-photon sources [3, 5], implementation of quantum random walks in an optical lattice , quantum simulation of complex spin systems  and the creation of entangled many-particle states . All these proposals are based on the dipole blockade mechanism where the strong Rydberg dipole-dipole interactions control or block a second Rydberg excitation following a first one. The Rydberg excitation blockade was realized in clouds of cold atoms  as well as in a Bose Einstein condensate . In addition the excitation of two individual atoms in the Rydberg blockade regime was recently performed [11, 12] and their entanglement demonstrated [13, 14].
The scalability of a quantum computer based on the long-range interactions of Rydberg atoms will rely on the realization of an array of trapped atoms . An optical lattice loaded with one atom in each site, such as the Mott insulator phase of ultracold bosonic atoms, represents the realization such an array. Additional crucial issues to be solved in order to realize this quantum computation configuration are the initialization and readout operations on a single site of the lattice. The preparation of a Mott insulator relies on an apparatus having a large optical access . Such optical access is also required in order to achieve the high quality control of atomic excitations required for the quantum computation operations.
This work reports on Rydberg spectroscopy performed on cold 87Rb atoms in a MOT. The experiments are performed within a Bose-Einstein condensation apparatus based on a quartz cell, used for in previous optical lattice investigations . Because the dipole blockade mechanism is modified by weak electric fields  we present an investigation of the atomic response to external electric fields at the mV/cm level. We present an original approaches applied in order to reach a level of control of Rydberg excitation for ultracold atoms as similar to that reached in Ref. . Our control will be of some use for subsequent work on the Rydberg excitation of a Bose-Enstein condensate loaded into an optical lattice.
Our Rydberg detection scheme is based on the ionization of Rydberg states by an electric field. In fact our apparatus allowed measurements of ions generated from MOT and BEC photoionization, with a large detection efficiency . In contrast to Ref.  in the present investigation the plates used to apply the ionizing electric field are located outside the quartz cell. Screening of this electric field was directly measured on the Rydberg excitation spectra. This effect is due to the presence of charges on the cell walls, however the source of such charges is not well defined. We demonstrate that even if the voltage applied to the outside of the cell is partially shielded by the charges on the quartz walls, a high level of control is achieved for the electric field acting on the atoms. Care must be taken not to charge the cell due to the prolonged exposure to high voltages. The lifetime of the wall charges is around ten minutes, therefore the electric field was switched for a time shorter than the charge relaxation time.
In order to measure precisely the atomic Rabi frequencies associated with the applied laser light, we measured the Autler-Townes splitting of the Rydberg excitation spectra as in Refs. [18, 19]. The reported spectra are modified by the electric field generated by the ions produced by the laser excitation, as pointed out in Refs. [20–22]. A precise control of the ion production is required for a controlled dipole blockade.
Section 2 introduces the relevant atomic energy levels and the two-photon laser interaction producing the Rydberg excitation. Section 3 describes the experimental configuration for cold atom production, their Rydberg state preparation and their detection by ion collection. Section 4 presents examples of observed Rydberg spectra. The spectra modification produced by the applied electric fields demonstrates the presence of charges on the cell walls following a continuous application of voltage on the external plates. This disturbance is avoided by applying short duration voltage pulses. The measurement of the Rydberg state Stark maps allowed us to calibrate the applied electric field. Autler-Townes spectra are measured and their deformation by the ion generated electric field is analyzed through a simple model. Section 5 presents our conclusions.
2. Atom-laser interactions
87Rb atoms in the 5S1/2 (F = 2) ground level, denoted as |g〉 with zero energy, are excited to Rydberg state by means of 2-photon absorption, as shown in Fig. 1. The 62P3/2 (F = 3) intermediate state, denoted as |e〉 with energy Ee and decay rate Γe = 8.9 ×106 s−1, is excited by 421 nm blue radiation. This 421 excitation is characterized by frequency νbl ≈ Ee/h, detuning δbl = νbl – Ee/h, Rabi frequency Ωbl, all of them to be measured in MHz. A second infrared (IR) laser at 1004–1020 nm is required to reach Rydberg states n2S (J = 1/2) and n2D (J = 3/2, 5/2), denoted as |nL〉, with principal quantum number n = 30 – 80, having an energy EnL and decay rate ΓnL. The parameters associated with this IR excitation are the frequency νIR ≈ (EnL – Ee)/h, detuning δIR = νIR – (EnL – Ee)/h, Rabi frequency ΩIR. The one photon transitions occur at δbl ≈ 0 and δIR ≈ 0, respectively. The sequence of the two processes produces the |g〉 → |e〉 → |nL〉 two-step excitation. The two-photon direct excitation |g〉 → |nL〉 takes place for νbl +νIR ≈ EnL/h, or alternatively δbl +δIR ≈ 0.
The ΓnL effective decay rate of the nL Rydberg level is given by the sum of the Γ0, the total spontaneous emission rate, and ΓBBR, the depopulation rate induced by black body radiation (BBR) 
The A(nL → 62P3/2) spontaneous decay rate from the Rydberg level to all the Zeeman states of the 62P3/2 level determines the transition dipole moment, appearing in the definition of the ΩIR and quantities. The atomic parameters for the few Rydberg states investigated are listed in Table 1.
The Rabi frequencies of the |g〉 → |e〉 → |nL〉 transitions depend on the quantum numbers of the atomic states composing the excitation sequence. For the |g〉 =52S1/2(F = 2) and |e>=62P3/2(F′ = 3) states the quantum numbers are the hyperfine ones |F,mF〉. Instead for the Rydberg states where the hyperfine splitting is small, the states are characterized by the J,mJ quantum numbers. As a consequence the blue and IR Rabi frequencies should be calculated in two different bases, |I,J,F,mF〉 to be denoted by the F,mF subscript and |I,mI, J,mJ〉 to be denoted by the I,J subscript. For instance in order to derive the atomic coupling with the IR laser as in Fig. 1, the intermediate 62P3/2(F = 3, mF = 2) state excited by the blue laser should be decomposed into the following states of the |I,mI, J,mJ〉 basis:Fig. 1 the laser excitation for the |g〉 → |e〉 → |n2D5/2,3/2〉 transitions in the case of blue and IR laser fields with linear polarization along the local magnetic field. The following excitation paths are reported for the 52S1/2 → 52P3/2 → n2D two-photon excitation: 18].
The absorption of a 421 nm photon by an atom in the 62P3/2 state ionizes the rubidium atoms with an ionization cross-section of 4.7 Mbarn , while the cross-section for absorption of 1 μm photon from the n ≈ 50 Rydberg states is very small, 4.5 × 10−5 Mbarn for 502S and 1.2 ×10−2 Mbarn for 502D . We calculated the average number of ions produced by the two-step photoionization pulse from the solution of the master equations describing the atomic interaction with the laser pulses introduced in . As an example the 62P3/2 ionization probability for a 10 μs blue laser pulse is 1. ×10−3 s−1 for a Ibl = 30 W/cm2 blue laser intensity. In addition, for long duration laser pulses the Penning ionization caused by the interaction-induced motion in cold Rydberg gases is an additional ion source .
The atomic absorption spectrum is modified by the presence of electric fields either applied by external sources or internally generated. The electric field polarizabilities of Rb atoms in Rydberg states were measured by Sullivan and Stoicheff in refs. [27, 28] respectively for the 2S and 2D states. For instance the scalar polarizability of the 552S state is 50(6), for 552D5/2 the scalar and tensorial polarizabilities are respectively 139(8) and 254(10), and for 552D3/2 85(3) and 82(3) respectively, all polarizabilities are in MHz/(Vcm−1)2 units. The ions generated by laser photoionization of rubidium atoms create an electric field which modifies the absorption of the atoms remaining in the MOT. The MOT ion content is very small, a maximum of one ion per thousand atoms. However at a distance of 1 μm the electric field due to an ion is 0.15 Vcm−1, which represents a −4.4 MHz shift for an atom in state 552D5/2, mJ = 5/2, a large value compared to the ≈1.5 MHz natural broadening of the 62P3/2 → 552D5/2 transition. The ion electric field is inhomogeneous over the atomic cloud, and we calculated an average value of the electric field acting on the rubidium atoms by supposing that the ions are uniformly distributed within the cold atom cloud. Because the ion number created by the photoionization increases within the laser pulse length, we based our analysis on the pulse mean number. The ions created by the laser irradiation may escape from the atomic cloud under the action of the internal electric fields produced by the electrons and ions, and the escape time should be compared to the Rydberg excitation time.
In a three-level system the saturation of one transition by a strong laser field, i.e. a large Rabi frequency, produces a strong modification of the absorption spectrum on the second transition. Consequence of this strong coupling is the well known Autler-Townes splitting . We investigate the Autler-Townes splitting produced by a strong blue laser and monitor it on the IR transition. If the blue laser is resonant with the |g >→ |e > transition, the IR transition is splitted into two components separated by the blue laser Rabi frequency, Ωbl, corresponding to the Autler-Townes splitting. For a blue laser beam detuned from the |g >→ |e > resonance by δbl, the Autler-Townes modification of the spectrum leads to absorption at the following values of the IR detuning9]. Owing to the dipole blockade, in our experimental investigation the efficiency of excitation to the Rydberg state is depressed and is lower than that predicted from the laser excitation of a single atom. The dipole blockade process is modified into an antiblockade by the Autler-Townes splitting produced by the blue laser, because one component of that splitting, as reported by , is shifted towards the resonance for the excitation of a second atom to the Rydberg state.
The MOT/BEC apparatus uses two quartz cells, collection and science respectively, horizontally mounted on a central metallic structure [16, 17]. We operate with a MOT having a small size around 50 μm and containing 105 atoms at the ≈ 1.5 ×1012 cm−3 atomic density, in order to investigate conditions similar to those created in a Bose-Einstein condensate.
The 421 nm blue radiation is generated by doubling a MOPA laser (TOPTICA TA 100, with output power 700 mW) with a TOPTICA cavity (output power 60 mW). An infrared (IR) laser between 1000 and 1030 nm allows ionization or atomic excitation to states with quantum number n between 30 and the continuum. High power and frequency stability of the IR radiation is achieved by injection locking a diode on an external cavity (output power 40 mW) into a Sacher TIGER laser (output power 250 mW) where the grating is replaced by a mirror. Both lasers systems, having a line-width smaller that 1 MHz, were locked using a Fabry Perot interferometer where a 780 nm laser locked to the Rb resonance acts as a reference . Both blue and IR beams were focused to a waist larger than the atomic cloud size, the minimum being 100 μm in order to maintain the cloud within the beam waist in presence of fluctuations in the spatial position of the cold atomic cloud. The blue/IR laser beams were applied as a pulse having a 0.5–10 μs duration with a gaussian rise time of 0.08 μs controlled by an acousto-optic modulator.
The MOT magnetic quadrupole field (72 G/cm along the strong axis) was not switched off during the Rydberg excitation phase. Owing to the small MOT size the magnetic field contributed less than 0.2 MHz to the observed linewidths. The polarizations of both blue and IR lasers were linear and parallel to each other along the strong axis of the quadrupole.
The Rydberg atoms are ionized and then detected by applying, just after the Rydberg excitation pulse, an electric field to the cell plates shown in Fig. 2. Experimental results shown in the following SubSection 4.2 provide evidence for the formation of electric charges on the cell walls creating uncontrolled electric fields. In order to avoid the presence of these wall charge, the Rydberg field ionization was based on an electric field pulse with a rise time of 700 ns and few μs duration applied to the copper plates outside the cell. The ion collection scheme is shown in Fig. 2. In previous work  we measured a high collection efficiency Th = 0.35(10) which includes both the fraction of the produced charges transported to the channel electron multiplier (CEM) and the multiplier detection efficiency. To avoid saturation of the detection system, for the ion spectra reported here a low collection efficiency Tl = 0.03(1) was obtained with the electric field pulse applied only to the plates located far from the CEM.
4.1. Rydberg spectra
We investigated the range of Rydberg energy levels we could tune the IR laser to. For this purpose, following excitation to the Rydberg state for the MOT trapped atoms, we measured the ions produced by the field ionization, with small contributions from photoionization, blackbody radiation absorption and Rydberg Penning ionization. Typically we acquired Rydberg spectra by scanning the frequency of the IR laser at fixed frequency of the blue laser. Figures 3 and 4 reports the spectra observed on the produced ions as a function of the IR laser frequency scanned around the the resonant frequency for the Rydberg excitation from the 62P3/2(F = 3) state. Figure 3 shows the spectrum recorded on the collected ions following the 602S1/2 and 502D3/2,5/2 excitations, respectively.
For the ion signal spectra of Fig. 4 corresponding to the 812D3/2,5/2 excitation, the top spectrum was obtained with no voltage applied to the cell external plates. Because the blue laser was detuned by 60 MHz from the 52S1/2(F = 2) → 62P3/2(F′ = 3) transition, two-photon and two-step signals are present on the spectrum. The two-photon 52S1/2(F = 2) → 812D5/2 transition is observed at δIR = −δbl = −60 MHz. The 52S1/2 → 812D3/2 two-photon transition is shifted to a lower frequency by the 812D fine splitting. The fine splitting between the 50D3/2,5/2 and 812D3/2,5/2 levels is in agreement with the predictions of Li et al. . The two-step signal associated to the 62P3/2(F′ = 3) → 812D5/2 transition is observed at δIR = 0 MHz. That associated for the 62P3/2(F′ = 3) → 812D3/2 transition is too weak for its observation.
4.2. Electric field generated by wall charges
We noticed that the voltage applied to the plates external to the quartz cell created charges on the cell walls that deformed the spectroscopic investigations. A clear example of the role played by the electric field due to the wall charges is shown in Fig. 4a. Rydberg spectra were recorded at different delay times following the application of a 3 kV voltage to the front and lateral plates for five seconds. The bottom spectrum, denoted by 0 time was recorded just after switching off the high voltage. Other spectra were recorded at later times, marked on the right side. A spectrum with clearly identified peaks (top one) was obtained only after 60 minutes, when the charges on the cell walls disappeared. From the analysis of the electric field splitting of the transition we derived that the initial electric field was around 0.2 V/cm and the lifetime of the wall charges was 12 minutes, as shown in Fig. 4b. In order to avoid the influence of these charges and maintain a good detection efficiency associated with the ion guide by the external plate voltage, we rapidly switched on the ion collecting voltages and only during the collection time, with typical pulses in the microsecond range. Formation of wall charges with a screening of an external electric field was reported in Ref. , where the main source of charge appeared to be ions and electrons produced by laser photodesorption at the cell surface. Electrical conductivity of the walls for different cells exposed to cesium vapour was investigated in , with the conductivity in glass cells connected to the cesium atoms physically adsorbed on the surface, this process being eliminated using sapphire cells. Notice that in our investigation the charges are produced on a fast time scale determined by the plate voltage risetime, and disappear on the ten minute timescale. We may suppose that the whole process is determined by field-assisted electron emission process, classified as exo-electron emission , and charge release from traps associated to rubidium atoms physically adsorbed on the walls. However the relative role of these processes on the time evolution of the wall charges remain obscure.
4.3. Externally applied electric fields
Avoiding an accumulation of charge on the walls we verified the degree of control over the electric field applied to the Rydberg atoms. Rydberg states are very sensitive to the presence of electric fields that produce either a broadening or a splitting of the excitation lines and therefore, at given laser parameters, a modification of the excitation efficiency. We have applied to the external plates low voltages, 10 Volts maximum, and monitored the frequency shift of Rydberg spectra. This constant electric field is applied just during the Rydberg excitation. Results for the measured Stark shift on the 772D3/2,5/2 excitation are shown in Fig. 5. The Stark map reports the measured position of the mJ levels for both D states versus the applied voltage. Notice that the mJ label is correct at zero electric field, while at larger values the electric field mixes the J = 3/2 and J = 5/2. Notice for an applied electric field around −0.09 Vcm−1 the presence of an avoided crossing of the states split by the electric field, similar to those investigated by Sullivan and Stoicheff . The continuous lines based on the polarizabilities by Ref.  allowed us to derive the conversion between the applied voltage (bottom axis) and the electric field acting on the atoms (top axis) denoting a minor electric field screening by wall charges. These Stark shifts provide evidence to show that our resolution for the applied electric field is at the 5 mV/cm level.
4.4. Ion created electric field
The Rydberg excitation spectra are modified by the presence of ions created by 62P photoionization and by black-body radiation ionization of Rydberg states, the Penning ionization rate being negligible for our experimental conditions. We have observed these modifications while probing the Autler-Townes splitting of the 62P3/2 state with an IR transition to the Rydberg state.
The observation of Autler-Townes splitting allows a direct measurement of the Rabi frequency for a two-state system, as applied in Refs. [18, 19], and the Rabi frequency precise knowledge is necessary for an efficient Rydberg excitation. Example of the Autler-Townes split spectra are shown in Fig. 6 for the two-photon 52S1/2 → 62P3/2 → 522S1/2 transition while scanning the IR laser frequency at constant δbl and Ωbl values. As expected, the Autler-Townes splitting of the IR absorption line into two components at large values of Ωbl was observed, in agreement with the Autler-Townes prediction.
In Fig. 7 the measured positions of Autler-Townes peaks are plotted versus the blue laser power/Rabi frequency at δbl = 0 and δbl = −10 MHz, in (a) and (b) respectively. The dashed lines in the figures are the theoretical predictions from the Eq. (7) by deriving the blue laser Rabi frequency from the laser power and beam waist. The measured peak positions show a systematic shift towards the red. Also plotted are the measured middle frequency of the Autler-Townes peaks. While the Autler-Townes theory predicts a constant position at fixed blue detuning, a systematic shift of the middle frequency towards the red was measured.
This shift originates from the Stark shift of the 522S1/2 Rydberg state associated to the ion created electric field. As the ions are originated mainly from the absorption of one blue photon from the intermediate 62P3/2 state, their number increases with the blue laser power leading to an increasing Stark shift. For instance at Ωbl = 60 MHz, two hundred ions are created by the blue laser photoionization and they produce a measured offset on our signals. We estimated the Stark shift produced by the ions (i) supposing all the ions remain within the cold atom cloud; (ii) determining an average electric field acting on the Rydbergs atoms for the case of ions uniformly distributed within the cloud volume. We verified that the electric repulsion between two ions is not large enough to expel them from the cloud within the excitation laser pulse. The Stark shift predicted by this simple model is represented by the central continuous line in Figs. 7a and 7b with a very good agreement with the measured shift, given the approximations included into our model. In addition the ions are not exactly distributed uniformly within the cloud and their spatial distribution follows the Gaussian profile of the blue laser. By calculating the sum of the Stark shift and of the Autler-Townes shifts we obtain the continuous lines of the Figures in good agreement with measured values. The observed broadening of the Autler-Townes peaks is in agreement with an inhomogeneous distribution of the electric field due to the ions.
The Autler-Townes spectra of Fig. 6 show an asymmetry in the peak heights. Equation (9) shows that for δbl = 0 the two peaks should have the same height, and instead the red shifted one is more intense. This asymmetry was observed also for the spectra recorded at δbl ≠ 0. We don’t have a clear explanation of the asymmetry. In the antiblockade experiments and theory by  and , respectively, this asymmetry is evidence of antiblockade. However owing to the dipole interaction in n2S states, in our case the antiblockade should lead to a larger height for the blue shifted peak. An asymmetry in the heights of the Autler-Townes peaks was also observed in  and interpreted as an imperfect control of the excitation laser detuning from resonance. Our control on the frequency of the excitation laser excludes such an occurrence. The role of the ion created electric field requires a careful analysis, and it may be postulated that the electric field modifies the Rydberg-Rydberg interactions and influences the antiblockade.
We have investigated Rydberg spectra of ultracold rubidium atoms in a MOT, in order to probe the electric field control present in a set-up based on a quartz cell. This apparatus has the large optical access which is required for Bose-Einstein condensation and the application of a three-dimensional optical lattice. The voltage applied to plates external to the cell in order to ionize the Rydberg states and to collect the ions, creates electric charges on the cell walls. Those charges remained on the walls with a typical ten minute lifetime. We avoided the creation of those charges by applying the voltage as a few microsecond pulse. Using this approach we performed investigations of excitation spectra to Rydberg states with n = 30–85 at various electric fields and demonstrated a control of the field at the few mV cm−1 level. This flexible control of the electric field matches the requirements of Rydberg excitation for quantum information applications.
The radiation used to excited the rubidium atoms from the 2S state to the 62P state also causes the photoionization of atoms in the 6P state. These ions generated an internal electric field which modifies the excitation spectra. Clear evidence of this internal electric field was obtained by studying the Autler-Townes spectra on the Rydberg excitation at increasing values of the blue laser light. This ion production causes a deformation of the Rydberg spectra and is unwanted for quantum information applications. For such a target, the ion production is drastically reduced by detuning the blue laser out of resonance with 52S → 62P transition, as experimentally verified. For a blue detuning of 1 GHz, the available blue/IR laser intensities lead to a 0.1 MHz two-photon Rabi frequency, large enough for efficient Rydberg excitation.
The extension of Rydberg excitation presented here to ultracold atoms spatially localized inside an optical lattice will be the topic of our future investigation.
We gratefully acknowledge funding by the EU STREP project “NAMEQUAM”, the EMALI European Network, a CNISM “Progetto Innesco 2007” and a MIUR PRIN-2007. The authors thank A. Chotia for help in a preliminary investigation.
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