Inverted Ladder Type Optical Excitation of Potassium Rydberg States

We present experimental results on the sub-Doppler Rydberg spectroscopy of potassium in a hot cell and cold atoms, performed with two counter-propagating laser beams of 405 nm and 980 nm in the inverted ladder-type system (4S1/2-5P3/2-nS1/2 and nD3/2;5/2). Such an inverted ladder type scheme is predicted to be without sub-Doppler electromagnetically induced transparency (EIT) feature in a thermal ensemble under the weak-probe approximation. Instead, we chose a strong probe field beyond the weak-probe approximation, and successfully observed a transparency window with a width narrower than 50 MHz. Our all-order numerical simulation is in satisfactory agreement with the experimental results. This narrow linewidth allows us to measure the energy levels of the Rydberg levels from n=20-70 with improved accuracy. The deduced ionization energy agrees with the previous measurements. Furthermore, on the cold ensemble, our experiment studied the mechanism of the trap loss induced by the two-photon Rydberg excitation. We found that the dephasing loss induced by the dipole-dipole interaction dominates the trap loss while the detuning from the intermediate state DeltaP>0 and the Rydberg state is occupied. Such a loss of the D state is stronger than that of the S state, because of its non-spherical symmetry. And, for p>0 and nearly no population on the Rydberg state, the perturbation from the excitation fields results in a reduction of trap efficiency.


I. INTRODUCTION
A Rydberg atom, which is an excited atom with one or more electrons in a high principal quantum number (n) state. Because of its extremely large polarizability, it has gained growing interest recently. Particularly, for quantum information processing, such a controllable large polarizability introduces many advantageous characteristics including strong dipole-dipole interactions that scale as n 4 and long radiative lifetimes that scale as n 3 . The controllability of the dipole-dipole interactions in Rydberg systems makes neutral atomic qubits unfold extraordinary potential to compete with trapped ion qubits as building block of quantum gates [1][2][3][4]. Meanwhile, the Rydberg dressed ensemble, also as a playground of collective phenomena, sheds new light on quantum simulation [5][6][7][8] and enhances the optical non-linearity induced by two-photon atomic coherences for quantum optics applications [9][10][11][12][13][14].
Since many works with optical trapped neutral atoms systems had contributed in improving the fidelity of qubit gate operations, one of the outstanding challenges in encoding qubits is the implementation of quantum nondestructive qubit state measurements without loss [15]. Besides using spatial localization to focus on one specific atom, using heteronuclear qubits is an improved method to mitigate crosstalk in neutral atom array experiments for the reason that they allow the state measurements possessing cross entanglement of two different atomic species located in the same trap, or nearby traps. The feasibility of this scheme has been discussed in [16][17][18], and experimental research relevant to heteronuclear atom qubits has been reported in Rubidium (Rb) isotopes [19]. Aside from the suggested Rb-Cs configuration, potassium and rubidium (K-Rb), is another possible candidate for the heteronuclear Rydberg qubits, in which both species share a similar cooling laser system. The two-body interaction in Rydberg-dressing schemes has been theoretically studied in [20]. Meanwhile, the Rydberg dressed fermionic isotope of potassium 40 K could provide richer collective phenomena and deeper insight for strongly correlated physics [21,22]. However, the Rydberg excitation on potassium, which is essential for the future K-Rb heteronuclear Rydberg interaction, was less studied and reported.
The species most commonly used for Rydberg experiments are alkali metals. However, there is rare work with K. Thus, more comprehensively, we experimentally studied the optical excitation of K Rydberg states using both hot and cold atoms, together with numerical simulation comparison. We measured EIT spectra using two-photon excitation with an inverted ladder type configuration (λ c > λ p ), where the wavelength of the probe field (405 nm) is much shorter than that of the coupling field (980 nm). The inverted scheme is particularly suitable for the future realization of multiqubit gates [1]. The coupling laser system at the wavelength can be benefited from the well-developed power amplifier with a power up to watt level in the near-infrared range [23]. Towards the heteronuclear Rydberg atoms interaction applications, such a high-power laser also acts as an optical dipole trap for the ultracold atomic ensembles of K and Rb.
Despite the inverted ladder type scheme in hot atomic ensembles was known to be lack of sub-Doppler feature, such as EIT, in the weak probe approximation using simple three-level model [24], however, the sub-Doppler feature was explicitly observed in our experiment. Thus, we perform theoretical simulation beyond the weak probe approximation to compare with the experimental observations. Our excitation scheme was also performed with a cold ensemble in a magneto-optical trap (MOT) using the trap loss as detection signal. The two-photon excitation with the normal ladder scheme (λ c < λ p ) in cold Rydberg ensemble was reported in [25]. The statedependent trap loss was studied in our experiments to provide the information for the attempts at Rydberg dressing experiments. The interaction of cold Rydberg atoms has been realized with atom pairs [26] and optical lattices [6,27], where atoms are orderly distributed. In contrast, in a homogeneous distributed atomic cloud, such as MOT or Bose-Einstein Condensate (BEC), an unexpectedly atom loss that has been observed in many experiments poses a challenging task, and the mechanism behind remains unclear. Only recently, A. D. Bounds et al. [28] reported a stable Rydberg-dressed MOT of Sr with a lifetime of several ms at a temperature < 1 µK. In our experiment, we employed the steady state approach to show that the Rydberg aggregation inducing avalanche dephasing might be the major origin of the loss.

II. THEORETICAL MODEL
Two-photon excitation is widely used to excite the atom to the Rydberg state in a three-level ladder-type system. It is particularly useful in those cases where one-photon excitation requires energy of deep UV wavelength or the excited Rydberg states has the same parity with the ground state. The two-photon atomic coherence, resulted from a coherent interaction of the coupling and probe lasers with atoms, introduces a variety of interesting phenomenon in the ladder-type Rydberg atom, such as EIT [29], electromagnetically induced absorption (EIA) [30], and Autler-Townes splitting effect. The ladder-type EIT takes advantage of the dramatic changes in the optical properties to achieve high-resolution Rydberg spectroscopy and to demonstrate a direct nondestructive optical detection of highly excited Rydberg states [31]. More complex phenomenon were also studied taking noncoherent effects into account [32].
The signals resulted from the two-photon excitation in a ladder-type three-level atoms include two effects: two one-photon resonances (two-step) and two-photon coherent excitation. They can be separated in the calculations under the weak-probe approximation. No Doppler-free feature is predicted to be observable in the inverted ladder systems [33][34][35] under such an approximation. In a more realistic experimental condition, the weak-probe approximation can be inadequate, thus we take all-order numerical calculation in our theoretical simulation. The density matrix is calculated numerically without any approximation to take into account the high order effects of the coupling and probe laser strengths. Although the actual states involved in our experiment are more than three, as shown in Fig. 1, we simplify it using an equivalent three-level system to obtain an effective steady state solution. All the additional decay channels, such as 4P state that has a fast decay rate to the 4S ground state, are treated as part of the 3→1 relaxation channel between the Rydberg state and the ground state. In the comparison with the experimental results, such an equivalent three-level system is found to be reliable approach for describing the complicated systems without losing any essential characters.
The simplified ladder configuration used in our simulation is shown in the left of Fig.1. The optical Bloch equations arė The levels |1 , |2 , and |3 , are corresponding to the 4S 1/2 , 5P 3/2 , and nS 1/2 states. The weak probe field and the strong coupling field are tuned close to the lower |1 -|2 transition and the upper |2 -|3 transition, respectively. The respective fields are denoted by: wavelength λ, Rabi frequency Ω, and detuning ∆. The spontaneous decay rate of the intermediate state 5P 3/2 (Γ 21 ) is around 7.35 MHz, which is mainly attributed to three decay channels via 5S 1/2 , 3D 3/2 and 4S 1/2 . The spontaneous decay rate Γ 32 is calculated to be 0.0017 MHz.
While the decay of the Rydberg state back to the ground state is primarily through the cascade nS→4P→4S cascade transition, the spontaneous decay rate Γ 31 is calculated to be 0.028 MHz. In our effective three-level model, Γ 31 also serves as an effective parameter including all the relaxation channels from the Rydberg state, such as collision quench and transit effects. It was manually adjusted for a best-fitting with the experimental results, and found to be ∼30 MHz that is much larger than the calculated rate from the radioactive relaxation. The dephasing rates, γ nm , are taken to be Γ nm /2 supposing the laser linewidth δω∼0. However, for that related to the open decay channel, such as γ 32 that dominates the linewidth of the EIA feature was also adjusted for a best-fit with the experimental results. The parameters used in our simulation are typically: In a hot cell with a Doppler-broadened medium, the probe transmission signal must be integrated over Maxwell-Boltzmann velocity distribution. For an atom moving with a velocity v in the same direction as the probe beam, in a coupling-probe counter-propagating configuration, the probe laser seen by the atom is bluedetuned (∆ p +v /λ p ) and the coupling laser is red-detuned where In Fig. 2, it evidently describes how the atoms with different velocities contribute the sub-Doppler feature to both non-inverted and inverted ladder-type cascade excitation with the wavelength mismatching. The upper parts are the density plots in terms of atomic velocity and probe beam detuning. The lower parts are the integrals of all the velocity groups and the simulated observable signals. The solid lines are the absorption of the probe beam with the coupling beam, and the dashed lines are without the coupling beam. Our experiment is to utilize the modulation transfer technique (see III) to measure the differential signal between the ON/OFF of the coupling beam, and to remove the large Doppler background in the probe signal. Thus, the Doppler backgrounds have been subtracted from all the simulation presented in the following discussion.
As shown in the far left picture (non-inverted) in Fig. 2, a narrow sub-Doppler window can clearly emerge in the non-inverted ladder system under all kinds of the conditions of probe beam power, even with a weak probe beam. However, in the inverted ladder system as shown in Fig. 2(a), which is with the same parameters, but exchanging the wavelengths of probe laser and coupling laser, no sub-Doppler feature can be observed anymore, even with a strong coupling beam (Ω p =0.2 MHz and Ω c =12 MHz). It agrees with the prediction under the weak-probe approximation. In Fig. 2(b), with a stronger probe beam (Ω p =1 MHz), a relative wide sub-Doppler feature appears in the absorption side. In Fig. 2(c), while the probe beam are even stronger (Ω p =8 MHz), an EIT feature emerges to result in a complicated profile as the interference between transparency and absorption. It should be noticed that the sub-Doppler width in the inverted systems is much wider than that of the noninverted systems.
In both of the non-inverted and inverted schemes, the sub-Doppler window appears in the situation, where the two-step condition, i.e.∆ c +∆ p =(ω p -ω c )v/c, is satisfied. Yet the size and the width of the transparency window is severely influenced by the wavelength ratio [36]. Based on our simulation, the inverted ladder types are certainly at unfavorable situations for narrowing the coherence window. That explains why they are expected to be vanished under typical weak-probe approximations. However, beyond such an approximation and with all-order numerical calculations, a sub-Doppler feature has been predicted to be feasible by [37]. The sub-Doppler feature can be a transparency window, an absorption dip, or a combination of both, as experimentally demonstrated by [24,38]. Figure 3 illustrates the simulated sub-Doppler features using the parameters mentioned above. A good agreement between our experimental observations and numerical simulation was presented. It is initially an absorption peak at low probe power region, then transformed to comprise a transparency window at high probe power region.

III. EXPERIMENTAL SETUP
The experimental setup shown schematically in Fig. 4 is composed of two tunable laser systems and a hot cell Rydberg spectrometer. The ultra-violate light at 405 nm, as a probe beam, is to excite 4S 1/2 → 5P 3/2 transition, while the near-infrared laser, as the coupling beam, with a tuning range from 970 nm to 990 nm is to excite 5P 3/2 → nS 1/2 (nD 3/2,5/2 ) transition. Both probe and coupling lasers are generated by home-made external cavity diode lasers (ECDL) with Littrow configuration. The lasers are capable of mode hop free range over 5 GHz with the current feed-forward technique. In order to further amplify the coupling laser power to ∼1 W, the near-infrared laser output from ECDL is injected into a GaAs based tapered amplifier chip (Coherent, TA-0976-2000) as a Master Oscillator Power Amplifier (MOPA) configuration. Then, the coupling beam passes through a polarization-maintaining optical fiber and is focused in the center of the cell with a beam diameter of 1.6 mm spatially overlapped with the probe beam with a beam diameter of 0.8 mm. This configuration ensures that the entire probe beam is covered by the coupling light. The maximum powers reaching to the interacting region of the cell are typically 25 mW for the probe (Ω p =21.2 MHz) and 350 mW for the coupling (Ω c =13.2 MHz). The coupling and probe beams are arranged in counter-propagation to reduce the width of the sub-Doppler window. The probe and coupling beams are linearly polarized in parallel to each other.
The vapor cell (Thorlabs, GC25075-K) is 7.18 cm in length, containing 93.3% 39 K and 6.7% 41 K, and its temperature is stabilized at 125 • C with a fluctuation less than 1 • C. The probe and coupling beams are separated after traveling through the vapor cell by two dichroic mirrors. The probe beam is detected using a photodiode to perform absorption spectroscopy. Meanwhile, the fluorescence signal is simultaneously monitored using a CCD camera with a narrow bandpass interference filter of 405 nm, 766 nm, or 460 nm. Our spectrometer utilizes modulation transfer techniques to remove Doppler-broadened profile and to improve the signal-to-noise ratio. The coupling laser is amplitude modulated by a mechanical chopper at 2-3 kHz, and the probe transmission is demodulated using a lock-in amplifier.
The coupling laser is locked to different frequencies for excitation to the Rydberg states (n=27-70) using software feedback control by cooperating with a high precision wavemeter (HighFinesse, WS6), which is capable of measuring the absolute frequency with an uncertainty less than 30 MHz and with a relative stability better than 1 MHz. The frequency of the probe laser is measured using either a second HighFinesse wavemeter or another wavemeter with a 1 GHz accuracy (Bristal 521).

IV. RYDBERG EXCITATION IN A HOT CELL
A typical experimental probe transmission spectrum is shown in the top of Fig. 5 with a 0.4 mW probe laser and a 300 mW coupling laser when the probe frequency scans over 4S-5P transition resonance. The fluorescence spectra of 404 nm and 460 nm are recorded simultaneously to help identify the population decaying channels. In the probe transmission spectrum, the Doppler background absorption is removed using modulation transfer technique. The left and right spectral signal are the excitation from F=2 and F=1 hyperfine structure of the 4S state, respectively. Both spectral signals include enhanced absorption part but only the F=2 includes a transparent window. The width of the transparent window is measured to be several tens of MHz. Despite the spectral feature manifests differently in the two transitions, they can be simulated based on the same rate mechanism, as described in Fig. 3 (b)-(c). For a specific transition, the competition between the strength of the transmission and absorption parts depends on Rabi frequencies of the probe and the coupling lasers, as shown in Fig. 6 and Fig. 7, respectively. We obtain a good agreement between our all-order numerical simulation and experiments for both the cases. Figure 6 represents that interference feature is changed from two absorptive peaks to a transparent window at higher probe Rabi frequency. It can be understood as the power broadening resulting in overlap and interference between the Autler-Townes doublet. In Fig. 7, the transmission dip clearly enhanced in the situation where the coupling Rabi frequency is smaller than 8 MHz. As the coupling Rabi frequency is increased, the absorption components grow up. It can be attributed to the transformation from EIT to Autler-Townes splitting due to the strong coupling intensity, thus the quantum interference is smeared out. The observed dephasing rate γ 31 is a few tens MHz, which is much larger than 12 kHz, estimated using the intrinsic lifetime of the states. This broadening might be caused by the transit effect, the optical pumping, the velocity-change collision in the hot cell, and the population trapping in the ground hyperfine states. Such a fast effective dephasing rate has also been observed and discussed in the other experiments [39,40] FIG. 6. The probe power dependence of EIT signal (4S 1/2 (F = 2) → 25S) for experimental results and simulations. The probe laser Rabi frequency Ωp varies from 3 to 22 MHz and the coupling Rabi frequency is fixed at Ωc=13 MHz with the relaxation parameters Γ21=7, γ21=3.5, Γ31=0.16, γ31=30, Γ32=0.0017, γ32=3.5 MHz.
The EIT signal for Rydberg states from 36S to 70S are also shown using a density plot in Fig. 8. Under the condition of the coupling power used in the experiment, there is no appearance of transparent window in the lower Rydberg states (n<60) and a transparency effect appears at higher Rydberg states. It is particularly interesting because of the similar trend for the dephasing rates ranged from 1-40 MHz.

V. LEVEL ENERGY MEASUREMENT
There are two primary excitation paths happening in a three-level cascade system: two-photon and two-step excitations. They can be distinguished by the frequency dependence between the coupling and probe laser frequency detunings. The photon energies in two-photon excitation need to satisfy the following conditions: On the other hand, the condition for two-step excitation, where two one-photon excitations are included, should satisfy the following conditions: where ∆ p (=f 12 − f p ) and ∆ c (= f 23 − f c ) are frequency detunings for the probe and coupling, respectively. To clarify the dominate path which results in the sub-Doppler feature in our observation, a series of the absorption spectrum of the Rydberg state n=26 with various coupling laser frequencies were taken. As shown in Fig.9, the frequency shift of the resonant probe laser is linearly dependent on the frequency detuning of the coupling laser with a slope of -2.448 (= −f 12 /f 23 ). It evidences that the sub-Doppler feature arises primarily due to the velocity group of atoms that are simultaneously resonant to both coupling and probe lasers, that is, the two-step excitation. In combination with the precisely measured 4S-5P transition frequency [41], the sub-Doppler signal with a good signal-to-noise ratio allows precision measurements for the Rydberg states up to 70S (Table.I). All of the uncertainties are limited by the accuracy of wavelength meter. Our results are in good agreement with previous two-photon spectroscopy. With several newly measured energy levels of the high n (> 55) states, our experimental results enable to derive the ionization energy (E i ). For this case with sufficiently large principal quantum numbers, the energies of Rydberg levels are given by: where R K is the Rydberg constant and only the loworder quantum defect δ(n, l, j) being taken into account under the approximation of the modified Rydberg-Ritz parameters [42] δ(n, l, j) The derived ionization energy of potassium is E i = 35009.87(6) cm −1 , which is in agreement with the previous reported values [43,44].

Rydberg States Energy Level Measurement
While measuring the energy level of Rydberg states, we lock coupling laser at a fixed frequency. Then scan probe laser to get spectrum by PZT. For this part of experiment, coupling beam power will always set at 300 mW and probe power will be 0.4 mW. A typical Rydberg state energy level spectrum is shown in Figure 17 FIG. 9. The frequency dependence between the probe frequency detune and coupling frequency detune, where A is for 4S 1/2 (F=2)-26S and B is for 4S 1/2 (F=1)-26S, along with linear fitting curve (red line).

VI. RYDBERG EXCITATION IN COLD ATOMS
As the discussion and experimental results shown above, it can be concluded that the sub-Doppler EIT signal appearing in the inverted ladder type scheme relies on the Doppler shift mechanism of the thermal atoms by the two-step excitation. With cold atomic ensemble, which enable only two-photon excitation by suppressing the two-step excitation because of the narrow velocity distribution in the cold ensemble.
In our experiment, the cold potassium atoms are trapped in a 39 K MOT with a total number of > 10 9 , corresponding to a number density of ∼ 10 10 /cm 3 . The temperature of the atomic cloud is ∼200 µK, which results in a Doppler width of only 1.2 MHz for 405 nm. In our MOT, the 766 nm cooling laser is tuned to 4S 1/2 (F = 2) → 4P 3/2 (F = 3) with a 12 MHz reddetuning and the repump laser is on the resonance of 4S 1/2 (F = 1) → 4P 3/2 (F = 2) transition. The total intensity of all the beams is 6 mW/mm 2 . The ratio of cooling and repump beam is 3:1. The gradient of the magnetic field is 10 G/cm.
Instead of using absorption signal to observe EIT in hot cell, the steady state trap loss is measured in the cold atoms by observing the 760 nm fluorescence signal from the MOT using a CCD camera while the probe and coupling beams are simultaneously sent to the MOT with beam sizes of 2.8 mm (FWHM) in a counter-propagating arrangement. As shown in Fig. 10, the trap loss signal of each measurement was obtained under the condition that the loss-capture equilibrium is reached, while both of the coupling and the probe lasers are stabilized at specific frequencies. The probe laser was side-locked to the saturation signal of the transition 4S 1/2 (F = 2) → 5P 3/2 with a frequency deviation of 1.5 MHz at 10 ms integration time. Hence, the probe frequency is ∼10 MHz (∆ p ) away from the 4S 1/2 (F = 2) → 5P 3/2 , and equivalent to ∼466 MHz away from 4S 1/2 (F = 1) → 5P 3/2 . The coupling frequency, measured by the wavemeter, was scanned over the frequency range of the transitions 5P 3/2 to 68D and 70S.
The trap loss signals resulted from the two-photon resonances with 4S 1/2 , F=2 (∆ p ∼ 0, on resonance case) and 4S 1/2 , F=1, (∆ p Doppler width, off-resonance case) allow the study to unravel the role of the coherent and the incoherent two-photon processes in the Rydberg excitation. The trap loss signal occurs when the ground state atom population decreases. The simplified rate equation of the trapped atom number in a MOT trap can be expressed as: where R is the loading rate, Γ is the background collision loss, and the γ x is the additional loss due to the Rydberg excitation. As the system reaches the steady state, the residual trapped atom number is: The Γ is 1.5 sec −1 , which was measured using the trap fluorescence rising time without the Rydberg excitation (i.e., far-detuned probe laser beam). This also serves a calibration for the other loss mechanisms under investigation.
The trap loss spectrum of both transitions are illustrated in Fig 10. The peak position of the trap loss satisfies the two-photon resonances equation ∆ p +∆ c = 0. To be compared between different transitions, the trap loss was normalized to the baslines of the coupling laser far away from the resonances. With the coupling laser power at 365 mW, in the ∆ p ∼10 MHz conditions, we observed that even µW of the probe laser power is high enough to cause a 100% loss, as shown in Fig. 10(a) and (c), where 48 µW and 5.6 µW was applied for 70S and 68D, respectively. In the off-resonance conditions (∆ p ∼466 MHz), a relative high power of the coupling laser, 6.5 mW, was used in Fig. 10(b) and (d) to induce an observable loss. And, the loss rate of both 70S and 68D are the same for the same probe power.
It had been found in many experiments using cold atomic ensembles that the trap decreases unexpectedly large. They might be originated from collision with ionized electron [45], spontaneous avalanche dephasing [46], and optical pumping [47].
In the off-resonance case where the detuning ∆ p is large, the population is hardly excited to the Rydberg states. Such a system should be treated with dressed state, and the dressed ground state |g is then written as: [47] where |g , |e , and |r denote the undressed ground state, intermediate state, and Rydberg states, respectively. The energy level is shifted by the ac Stark effect through the two-photon process. It turns out that the overall energy structure becomes not to be appropriate for trapping, which results in a reduction of the capture rate of the MOT. This explains why a much higher power is required and the similarity on the loss rate between S and D states. For ∆ p ∼ 0, a significant amount of population in the ground state will be transferred to the Rydberg state through an incoherent process, where the collision or ionization caused by the Rydberg state population should be taken into account. The additional ground state loss by the Rydberg excitation, γ x , including all the possible loss mechanisms mentioned earlier, can be expressed as: The first term is the optical coupling to the Rydberg state. It is proportional to the effective excitation rate, (Ω p Ω c ) 2 . Those atoms in MOT, which are excited to the Rydberg states after absorbing two photons, will obtain extra momentum capable of escaping from the trap. The loss induced by optical pumping [47] is also included in this part. The second term, proportional to the ionized free electron density n e [45], is found too small to be account for such a large loss [47]. The third term is spontaneous avalanche dephasing effect that is proportional to the excited Rydberg density n R and caused by the dipole-dipole interaction [48]. The excitation rates of the 70S and 68D calculated from the relevant transition rates are similar. As the experimental results shown in Fig. 10, under the condition of ∆ p ∼10 MHz, the loss rate of 68D is stronger than 70S by a factor of 8. Thus, the first and second terms, which are only related to the Rydberg excitation rate, provide insufficient explanation to the observed large difference of the loss rate between the S and D states. It implies that the third term, the dephasing induced by the dipole-dipole interaction with the nearby lower P states [48], should be responsible for such a large loss rate, because the anisotropic wave function and the dipole moment of the D state will cause a stronger dephasing than that of the spherically symmetrical S state.

VII. CONCLUSION
With a potassium hot vapor cell, we demonstrate a sub-Doppler EIT feature to emerge using two-step excitation even in an inverted ladder-type scheme. When the connection between the ground state and Rydberg states is linked by a probe field and a coupling field, the sub-Doppler feature in such a ladder-type scheme can also provide a Rydberg atom detection, as that of normal ladder-type schemes. The transparency window is with a width <50 MHz allowing high-resolution spectroscopy and good signal-to-noise ratio for the detection of high Rydberg states. The precision measurements of the energy level with an uncertainty better than 0.03 cm −1 are provided for the Rydberg states from 20S to 70S.
We developed the theoretical model using optical Bloch equations without the weak probe approximation. This model provides an excellent agreement with the experimental results on the probe laser spectrum and laser induced fluorescence spectrum. It shows that the Doppler distribution of atoms in the vapor cell plays an essential role in the inhomogeneous media to narrow the transparency window. The observed sub-Doppler feature is typically composed of absorption and transparency features dependent on the strengths of the probe and coupling fields. The strong correlation between the principle quantum number n of the states and the dephasing rates was also observed. The more pronouncing EIT in the high-n states implies that the longer lifetime of the higher Rydberg states reduces the dephasing rate and enhances the coherence, as predicated.
The two-photon excitation was also performed in cold potassium MOT through the detection of trap loss signal. The cold ensembles reduce the two-step excitation effect and enable only two-photon excitation. The mech-anisms behind the unexpectedly large trap loss in the cold Rydber atoms were then studied. For the case of far-detuning, the loss is found to be resulted from the perturbation to the levels related to the laser tapping scheme, due to the two-photon resonance. For the case of that both pumping and probe lasers are on resonances (two-step resonance) we confirmed that the dephasing caused by the dipole-dipole interaction plays a major role. Therefore, because of the symmetry of the S and D states, the loss rates of them exhibit a significant difference. Our results provide a detailed study on the potassium Rydberg excitation for the future quantum technol-ogy applications using the Rydberg-dressed potassium, especially the heteronuclear qubits.