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Photoionization spectrum of 85RbCs molecules produced by short range photoassociation
Journal of Quantitative Spectroscopy & Radiative Transfer 166 (2015) 36–41
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Photoionization spectrum of 85RbCs molecules produced by short range photoassociation Zhonghua Ji, Jinpeng Yuan, Yonggang Yang, Yanting Zhao n, Liantuan Xiao, Suotang Jia State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, People's Republic of China
a r t i c l e in f o
abstract
Article history: Received 11 May 2015 Accepted 18 July 2015 Available online 28 July 2015
We present photoionization (PI) spectrum of ultracold ground state 85RbCs molecules formed by spontaneous decay from J ¼ 1, v ¼8 rovibrational level of ð2Þ3 Π 0 short range excited state molecules, which are produced from a space-adjustable dark spontaneous force optical trap. PI spectrum is obtained by scanning PI laser when photoassociation laser is locked by utilizing transfer cavity technique based on an ultrastable He–Ne laser as a reference laser. We calculated vibrational distribution of RbCs molecules in metastable þ ground state and corresponding transition probabilities to RbCs ion in ð1Þ2 Σ þ state. An enlarged PI spectrum with relative clear peaks is assigned to v ¼ 24–33 vibrational levels of molecular ion state. The method we used in PI spectrum analysis is also adoptable for other states of RbCs molecules or other kinds of molecules. & 2015 Elsevier Ltd. All rights reserved.
Keywords: RbCs molecule Photoassociation spectrum Photoionization spectrum Transition probability
1. Introduction Ultracold polar molecules have attracted considerable attention in the past decades [1,2]. The permanent electric dipole moments of polar molecules give rise to anisotropic, long-range dipole–dipole interactions which can be tuned by applied electric fields [3]. This property, combined with ultracold atoms, offers abundant potential applications, such as controlled chemistry [4,5], precision measurement [6–8], quantum computation [9] and quantum simulation [10,11]. Direct laser cooling of molecules into the ultracold regime faces great challenge, though recent demonstrations of laser cooling show great promise [12–14]. An alternative approach to produce ultracold polar molecules is to start from precooled atoms by magnetoassociation [15] or photoassociation [16]. Considering the relative simple electric structure and available economic commercial lasers, heteronuclear alkalimetal molecules are widely investigated [17,18]. Among these
n
Corresponding author. Tel./fax: þ 86 3517113828. E-mail address: [email protected] (Y. Zhao).
http://dx.doi.org/10.1016/j.jqsrt.2015.07.008 0022-4073/& 2015 Elsevier Ltd. All rights reserved.
diatomic dimers, RbCs molecule is particularly interesting for these distinctive merits: Both exchange (2RbCs-Rb2 þCs2 ) and trimer formation (2RbCs-Rb2 Cs þCs or RbþCs2Rb) reactions are endothermic for ground-state RbCs molecules [19]. Moreover, the large electric dipole moment of 1.225 D [20] is easily aligned in the laboratory frame, meaning that only modest electric fields are required to realize significant dipole–dipole interactions. At last, since RbCs molecules (both 85 RbCs and 87RbCs) are bosons, such a system could be exploited for a BEC of polar molecules. As one of the earliest polar molecules investigated, the 85 RbCs molecules in metastable ground state are formed from photoassociative molecules in long range, and transferred to singlet ground state by incoherent stimulated emission pump-dump scheme [21]. Another elegant but much more complex coherent control techniques, two-photon stimulated Raman adiabatic passage (STIRAP) process, recently has been used to produce the rovibrational ground state 87RbCs molecules starting from Feshbach resonance molecules [22,20]. Especially, short range photoassociated RbCs molecules in ð2Þ3 Π 0 7 excited state attract many researchers' attention for its simplify and continuous formation scheme to singlet
Z. Ji et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 166 (2015) 36–41
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ground state molecules directly from ultracold atoms [23–28], just like the cases of LiCs [29], NaCs [30], KRb [31]. It needs to be declared that ð2Þ3 Π 0 7 state is a co-written label of ð2Þ3 Π 0 þ and ð2Þ3 Π 0 states. In our previous work [26], we investigated photoassociative formation of RbCs molecules in one vibrational state of ð2Þ3 Π state, and measured the corresponding molecular constant with a high sensitivity, such as rotational constant, distortion constant, and electric dipole moment. In this paper, we observe and analyze the photoionization þ spectrum of ultracold 85RbCs molecules in a3 Σ metastable ground state formed by spontaneous decay from one rovibrational level of ð2Þ3 Π 0 state. A photoassociated laser is used to produce the excited state molecules from two species cold atoms in a space-adjustable dark spontaneous force optical trap (SPOT), and then locked by transfer cavity technique. We þ calculate the distribution probabilities in a3 Σ state and the þ þ corresponding transition probabilities to RbCs ion in ð1Þ2 Σ state. An enlarged PI spectrum with relative large space between peaks (favorable for spectrum analysis) is analyzed and assigned based on our calculation.
sapphire laser system (MBR110, Coherent) with a typical linewidth of less than 100 kHz and output power up to 800 mW. The ionization laser in our experiment is provided by a pulsed dye laser pumped by 532 nm Nd: YAG laser at a repetition rate of 10 Hz. The pulsed laser can cover 680–760 nm with 8 ns pulse duration using Pyridine 2 dye molecule and is focused to the size of atomic clouds with a lens. The PA laser excites a pair of colliding 85Rb and 133 Cs atoms into a deeply bound level at ð2Þ3 Π short range, specifically the J ¼1, v ¼8, (4)0 rovibrational state correlated Rbð5P1=2 Þ þ Csð6S1=2 Þ atomic asymptote. Ground state molecules, formed from these excited molecules by spontaneous decay, are ionized by resonance enhanced multiphoton ionization (REMPI) and detected by a microchannel plate (MCP) using time-of-flight mass spectrum under an accelerated electric field (83 V/cm). The photoionized ions are detected, amplified, then monitored on an oscilloscope and recorded by a NI PCI1714 card following a boxcar integrator.
2. Experimental setup
Fig. 2 shows the photoassociation spectrum of the short range molecule state, which was initially assigned to be v ¼ 8, ð5Þ0 þ of ð2Þ3 Π state [26], but here replaced by ð4Þ0 with other quantum numbers unchanged based on Ref. [27]. Note that our final spectra analysis is robust with respect to small changes of the initial vibrational quantum numbers. The reference frequency in horizontal axial is 11 724.085 cm 1, chosen at J¼1 rotational state with the highest intensity. The inset is the enlarged view of J¼1 rotational state with a full width at half maximum (FWHM) of around 30 MHz. To investigate ground state molecule, we lock PA laser frequency at the J¼1 rotational state using a transfer cavity technique [35]. The transmission peak signals of He–Ne laser (SL-02, SIOS) and PA laser, acting as master laser and slave laser respectively, are recorded by a DAQ multifunction card (NI PCI-6014) when the cavity is scanned externally. A program based on LabVIEW software records the two lasers' peak signal independently, then calculate the relative position of master laser and slave laser. Feedback voltage is generated to make the relative position to a setting value, then the stability of He–Ne laser is translated to the PA laser. The longterm stability of He–Ne laser we used is less 6 10 9 (2.8 MHz) over 8 h. The measured PA laser frequency variation after locking is less than 4 MHz measured by error signal, which is much smaller than the FWHM of J¼1 rotational state. The long term stability of PA laser provides enough time to obtain photoionization spectrum of ground state molecules. Fig. 3(a) shows the photoionization spectrum of ground state molecules by scanning photoionization laser frequency while keep PA laser locked at J¼1 rotational state shown in Fig. 2. Since the linewidth of PI laser (0.1 cm 1) is larger than the spacing of rotational states, even the one of Xð0; 0Þ state (0.0166 cm 1 for spacing between J¼0 and 1 states, see Refs. [36,37]), it is impossible to distinguish rotational level. We find three obvious dips in Fig. 3(a), which are affected by some resonant transition lines of Cs and Rb atoms, shown in Fig. 3 (b). The number 2 in denominator means that the dye laser frequency agrees with the transition frequency over 2. These atoms in high-level state excited by one (two) dye laser
Most details of the apparatus have been described in our studies of ð2Þ3 Π excited state 85RbCs molecules in short range [26]. Here we only describe some key characters and new changes (see Fig. 1(a)). In previous work, ultracold 85Rb and Cs atoms are cooled and trapped in a normal dark SPOT, which can provide a cold sample with high atomic density and low collision rate [32]. Usually it cost us a lot of effort to make the two atom clouds overlapped, which is very necessary for production of heteronuclear molecules. Here we introduce a new method called space-adjustable dark SPOT for efficient production of RbCs molecules. Comparing with one mixed beam of repump beam and depump beam in previous optical arrangement, the main improvement here happens in the addition of another mixed beam in counter-propagation. The detail optical arrangement is described below. The Rb and Cs repump beams are combined together by polarizing beam splitter 1 (PBS 1) and two half-wave plates and then are blocked by a black dot of 5 mm in diameter in the center of combined beams. The Rb and Cs depump beams are combined together by another PBS 2 and two waveplates, and then fill the black dot in the combined repump beams. We divide the mixed repump and depump beams into two beams by the third PBS 3 and one half-wave plate and then make them irradiate atomic region in the opposite directions, shown in Fig. 1(a). Note that each beam has both repump beam and depump beam. With this optical arrangement, we can easily adjust relative space position of the two atom clouds and finally have an excellent overlap in dark SPOT. Fig. 1(b) shows the relative space movement of Rb and Cs cold atomic clouds in dark SPOT along horizontal direction when we change the power ratio of two repump (also depump) beams after PBS 3. The special optical arrangement for repump and depump beams make us to have nearly 100% overlap of the two atomic clouds. Fig. 1(c) shows the formation and ionization scheme of metastable ground state RbCs molecules. The photoassociation laser is provided by a continuous wave tunable Ti:
3. Results and discussion
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Fig. 1. Experimental scheme. (a) Brief diagram of optical elements near vacuum chamber. (b) Space movement of Rb and Cs atom clouds. The overlap can be easily adjustable when we change the power ratio of repump (also depump) beams after PBS 3 (see text) in the nearly opposite directions, shown in (a). (c) Formation and detection process of ultracold metastable ground state molecule. The mixed Rb and Cs atoms produced in (a, b) are photoassociated to þ RbCs molecules in J ¼1, v¼ 8, ð4Þ0 state of ð2Þ3 Π electric state followed by spontaneous emission to a3 Σ ground state, which is ionized to molecular ion þ in ð1Þ2 Σ state by REMPI. The potential energy curves are based on the data in Refs. [33,34].
Fig. 2. Photoassociation spectrum of v¼8, ð4Þ0 of ð2Þ3 Π excited state RbCs molecules.
photon (s) are then ionized by another PI photon to atomic ions, which are detected by MCP. The profile of PI spectrum obtained here is consistent with that obtained by Gabbnnini et al. [23–25], where Stark effect arising from static electric field was not eliminated and PA laser was only locked to a normal Fabry–Pérot interferometer. They proposed that the intermediate states in ionization þ process belong to ð3Þ3 Π and ð4Þ3 Σ electronic states. However, they did not give detailed discussion as PI spectrum were not the topics of those papers. Here we ignore the specific intermediate state in REMPI process, consider the þ þ transition from a3 Σ ground state to ð1Þ2 Σ molecular ion state when PA laser is locked at J¼1, v¼8, ð2Þ3 Π 0 rovibrational excited state. We use LEVEL program 8.0 [38] to calculate the wavefunctions and energies of vibrational states for the excited state, ground state, and molecular ion state based on the corresponding potential energy curves, which are taken from Refs. [33,34]. With the help of vibrational wavefunctions, we can further calculate the transition
probabilities between vibrational states of different potential energy curves. Fig. 4 shows the calculated transition probabilities from the v¼8, ð2Þ3 Π 0 excited PA state to the v¼0–29 vibrational þ states of a3 Σ state. These probabilities correspond to initial þ population distribution of different vibrational states on a3 Σ electronic state. It shows that ground state molecule population mainly distribute in the lowest decades vibrational states. þ We calculate transition probability from a3 Σ state distributþ ing in the range of v¼ 0 and v¼29 states to ð1Þ2 Σ molecular ion state by multiplying the initial population distribution. It needs to be noted that the ionization process contains two photons, the transition frequency between ground state to molecular ion state is two times larger than the value of dye laser frequency used in the experiment. The vibrational þ quantum numbers of ð1Þ2 Σ molecular ion state cover v¼21–74 in the scanning range of dye laser in Fig. 3. The data of PI spectrum and transition probability are available in supplemental files. Fig. 5(a) shows a small portion of Fig. 3(a) while Fig. 5(b) þ shows the corresponding transition probabilities from a3 Σ 2 þ state distributing in the range of v¼0–29 states to ð1Þ Σ molecular ion state. To compare with PI spectrum, transition þ þ frequency from a3 Σ state to ð1Þ2 Σ molecular ion state has been divided by number 2. We enlarge PI spectrum in this range for that the space between peaks is relatively larger, thus is favorable for spectrum analysis. The red solid line in Fig. 5(b) is smoothing results of the probability with point number of 30, which is the same as the number of vibrational states in ground state we have calculated. The smoothing results have been multiplied by 3 for the better comparison. For the nine peaks in Fig. 5(b), the corresponding transition final states (molecular ion state) are v¼24,…,33, which are shown on the top of Fig. 5(a). Take the first peak as an
Z. Ji et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 166 (2015) 36–41
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þ
Fig. 3. (a) Photoionization spectrum of a3 Σ ground state RbCs molecules when PA laser is locked at J ¼1 rotational state in Fig. 2. (b) Photoionization spectrum of Rb and Cs atoms in dark SPOT. The resonant transition lines are shown in the corresponding peaks, which agree with the dips of molecule photoionization spectrum in (a). The number 2 in denominator means that the dye laser frequency agrees with the transition frequency over 2.
Fig. 4. The calculated distribution probability of metastable ground state molecules by spontaneous decay when photoassociation laser frequency is locked at J¼ 1 rotational state in Fig. 2(a).
example, the ratio of transition probability to v¼24 and 25 þ states from a3 Σ ground state are 33.3% and 44.3%, respectively. The sum of transition probabilities to all other vibrational states is left 22.4%. The ratio for other cases is similar and can be obtained from supplement files if readers are interested. Comparing the measurement and calculated results, it shows that half parts of peaks in PI spectrum agree with calculated probability. Regards to the other half parts of peaks, we attribute this disparity to the complexity of PA state. There are strong mixtures between (4)0 and (6)1 states [24], which may affect the distribution of ground state molecules. In addition, the PA state may decay to high vibrational levels of singlet state via a multi-step process, from which the RbCs molecules can be ionized to RbCs þ by similar two-photon ionization process, or decay to low vibrational levels which are ionized to ions through absorption bands at 717 nm [39]. It is somewhat difficult to clarify this ionization scheme and
Fig. 5. (a) A portion of PI spectrum with relative clear peaks, shown in þ Fig. 3(a). (b) The corresponding transition probabilities from a3 Σ state þ distributing in the range of v¼ 0–29 states to ð1Þ2 Σ molecular ion state, mainly distributing in the range of v¼ 24–33 states. The red solid line is smoothing results with point number of 30 and magnify 3 times for the better comparison. The corresponding transition final state (molecular ion state) are shown on the top of (a). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
more comprehensive theory will be implemented in the future. 4. Conclusion To conclude, we have investigated the photoionization spectrum of metastable ground state molecules formed by
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spontaneous decay from J ¼1, v ¼8 rovibrational level of ð2Þ3 Π 0 short range excited state. Based on the available potential energy curves, we calculate energies of vibrational states for excited PA state, metastable ground state, and molecular ion state. Then we calculate the distribution of metastable ground state molecules and the transition þ probability from a3 Σ state distributing in the range of þ v ¼0 and v ¼29 states to ð1Þ2 Σ molecular ion state. An enlarged view of PI spectrum containing v0 ¼ 24–33 vibrational states of molecular ion is shown and half of peaks of PI spectrum agree with theoretical calculations. The PI spectrum analysis is meaningful for understanding population distribution of metastable ground state molecules and is also illuminating for other states, such as singlet ground state molecules, or other molecular PI spectrum. Future experiment will investigate the PI spectrum of singlet ground state molecules produced by the same intermediate excited state and STIRAP transfer to absolute rovibronic ground state molecules from nearly quantum degenerate atoms in optical dipole trap.
Acknowledgment The work was supported by the 973 Program (No. 2012CB921603), 863 Program (No. 2011AA010801), Natural Science Foundation of China (Nos. 61275209, 11304189, 61378015 and 11434007), NSFC Project for Excellent Research Team (No. 61121064), PCSIRT (No. IRT13076), the talent program of Shanxi and the NSF of Shanxi, China (No. 2014021004). Appendix A. Supplementary data Supplementary data associated with this paper can be found in the online version at http://dx.doi.org/10.1016/j. jqsrt.2015.07.008.
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Photoionization spectrum of 85RbCs molecules produced by short range photoassociation Zhonghua Ji, Jinpeng Yuan, Yonggang Yang, Yanting Zhao n, Liantuan Xiao, Suotang Jia State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, People's Republic of China
a r t i c l e in f o
abstract
Article history: Received 11 May 2015 Accepted 18 July 2015 Available online 28 July 2015
We present photoionization (PI) spectrum of ultracold ground state 85RbCs molecules formed by spontaneous decay from J ¼ 1, v ¼8 rovibrational level of ð2Þ3 Π 0 short range excited state molecules, which are produced from a space-adjustable dark spontaneous force optical trap. PI spectrum is obtained by scanning PI laser when photoassociation laser is locked by utilizing transfer cavity technique based on an ultrastable He–Ne laser as a reference laser. We calculated vibrational distribution of RbCs molecules in metastable þ ground state and corresponding transition probabilities to RbCs ion in ð1Þ2 Σ þ state. An enlarged PI spectrum with relative clear peaks is assigned to v ¼ 24–33 vibrational levels of molecular ion state. The method we used in PI spectrum analysis is also adoptable for other states of RbCs molecules or other kinds of molecules. & 2015 Elsevier Ltd. All rights reserved.
Keywords: RbCs molecule Photoassociation spectrum Photoionization spectrum Transition probability
1. Introduction Ultracold polar molecules have attracted considerable attention in the past decades [1,2]. The permanent electric dipole moments of polar molecules give rise to anisotropic, long-range dipole–dipole interactions which can be tuned by applied electric fields [3]. This property, combined with ultracold atoms, offers abundant potential applications, such as controlled chemistry [4,5], precision measurement [6–8], quantum computation [9] and quantum simulation [10,11]. Direct laser cooling of molecules into the ultracold regime faces great challenge, though recent demonstrations of laser cooling show great promise [12–14]. An alternative approach to produce ultracold polar molecules is to start from precooled atoms by magnetoassociation [15] or photoassociation [16]. Considering the relative simple electric structure and available economic commercial lasers, heteronuclear alkalimetal molecules are widely investigated [17,18]. Among these
n
Corresponding author. Tel./fax: þ 86 3517113828. E-mail address: [email protected] (Y. Zhao).
http://dx.doi.org/10.1016/j.jqsrt.2015.07.008 0022-4073/& 2015 Elsevier Ltd. All rights reserved.
diatomic dimers, RbCs molecule is particularly interesting for these distinctive merits: Both exchange (2RbCs-Rb2 þCs2 ) and trimer formation (2RbCs-Rb2 Cs þCs or RbþCs2Rb) reactions are endothermic for ground-state RbCs molecules [19]. Moreover, the large electric dipole moment of 1.225 D [20] is easily aligned in the laboratory frame, meaning that only modest electric fields are required to realize significant dipole–dipole interactions. At last, since RbCs molecules (both 85 RbCs and 87RbCs) are bosons, such a system could be exploited for a BEC of polar molecules. As one of the earliest polar molecules investigated, the 85 RbCs molecules in metastable ground state are formed from photoassociative molecules in long range, and transferred to singlet ground state by incoherent stimulated emission pump-dump scheme [21]. Another elegant but much more complex coherent control techniques, two-photon stimulated Raman adiabatic passage (STIRAP) process, recently has been used to produce the rovibrational ground state 87RbCs molecules starting from Feshbach resonance molecules [22,20]. Especially, short range photoassociated RbCs molecules in ð2Þ3 Π 0 7 excited state attract many researchers' attention for its simplify and continuous formation scheme to singlet
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ground state molecules directly from ultracold atoms [23–28], just like the cases of LiCs [29], NaCs [30], KRb [31]. It needs to be declared that ð2Þ3 Π 0 7 state is a co-written label of ð2Þ3 Π 0 þ and ð2Þ3 Π 0 states. In our previous work [26], we investigated photoassociative formation of RbCs molecules in one vibrational state of ð2Þ3 Π state, and measured the corresponding molecular constant with a high sensitivity, such as rotational constant, distortion constant, and electric dipole moment. In this paper, we observe and analyze the photoionization þ spectrum of ultracold 85RbCs molecules in a3 Σ metastable ground state formed by spontaneous decay from one rovibrational level of ð2Þ3 Π 0 state. A photoassociated laser is used to produce the excited state molecules from two species cold atoms in a space-adjustable dark spontaneous force optical trap (SPOT), and then locked by transfer cavity technique. We þ calculate the distribution probabilities in a3 Σ state and the þ þ corresponding transition probabilities to RbCs ion in ð1Þ2 Σ state. An enlarged PI spectrum with relative large space between peaks (favorable for spectrum analysis) is analyzed and assigned based on our calculation.
sapphire laser system (MBR110, Coherent) with a typical linewidth of less than 100 kHz and output power up to 800 mW. The ionization laser in our experiment is provided by a pulsed dye laser pumped by 532 nm Nd: YAG laser at a repetition rate of 10 Hz. The pulsed laser can cover 680–760 nm with 8 ns pulse duration using Pyridine 2 dye molecule and is focused to the size of atomic clouds with a lens. The PA laser excites a pair of colliding 85Rb and 133 Cs atoms into a deeply bound level at ð2Þ3 Π short range, specifically the J ¼1, v ¼8, (4)0 rovibrational state correlated Rbð5P1=2 Þ þ Csð6S1=2 Þ atomic asymptote. Ground state molecules, formed from these excited molecules by spontaneous decay, are ionized by resonance enhanced multiphoton ionization (REMPI) and detected by a microchannel plate (MCP) using time-of-flight mass spectrum under an accelerated electric field (83 V/cm). The photoionized ions are detected, amplified, then monitored on an oscilloscope and recorded by a NI PCI1714 card following a boxcar integrator.
2. Experimental setup
Fig. 2 shows the photoassociation spectrum of the short range molecule state, which was initially assigned to be v ¼ 8, ð5Þ0 þ of ð2Þ3 Π state [26], but here replaced by ð4Þ0 with other quantum numbers unchanged based on Ref. [27]. Note that our final spectra analysis is robust with respect to small changes of the initial vibrational quantum numbers. The reference frequency in horizontal axial is 11 724.085 cm 1, chosen at J¼1 rotational state with the highest intensity. The inset is the enlarged view of J¼1 rotational state with a full width at half maximum (FWHM) of around 30 MHz. To investigate ground state molecule, we lock PA laser frequency at the J¼1 rotational state using a transfer cavity technique [35]. The transmission peak signals of He–Ne laser (SL-02, SIOS) and PA laser, acting as master laser and slave laser respectively, are recorded by a DAQ multifunction card (NI PCI-6014) when the cavity is scanned externally. A program based on LabVIEW software records the two lasers' peak signal independently, then calculate the relative position of master laser and slave laser. Feedback voltage is generated to make the relative position to a setting value, then the stability of He–Ne laser is translated to the PA laser. The longterm stability of He–Ne laser we used is less 6 10 9 (2.8 MHz) over 8 h. The measured PA laser frequency variation after locking is less than 4 MHz measured by error signal, which is much smaller than the FWHM of J¼1 rotational state. The long term stability of PA laser provides enough time to obtain photoionization spectrum of ground state molecules. Fig. 3(a) shows the photoionization spectrum of ground state molecules by scanning photoionization laser frequency while keep PA laser locked at J¼1 rotational state shown in Fig. 2. Since the linewidth of PI laser (0.1 cm 1) is larger than the spacing of rotational states, even the one of Xð0; 0Þ state (0.0166 cm 1 for spacing between J¼0 and 1 states, see Refs. [36,37]), it is impossible to distinguish rotational level. We find three obvious dips in Fig. 3(a), which are affected by some resonant transition lines of Cs and Rb atoms, shown in Fig. 3 (b). The number 2 in denominator means that the dye laser frequency agrees with the transition frequency over 2. These atoms in high-level state excited by one (two) dye laser
Most details of the apparatus have been described in our studies of ð2Þ3 Π excited state 85RbCs molecules in short range [26]. Here we only describe some key characters and new changes (see Fig. 1(a)). In previous work, ultracold 85Rb and Cs atoms are cooled and trapped in a normal dark SPOT, which can provide a cold sample with high atomic density and low collision rate [32]. Usually it cost us a lot of effort to make the two atom clouds overlapped, which is very necessary for production of heteronuclear molecules. Here we introduce a new method called space-adjustable dark SPOT for efficient production of RbCs molecules. Comparing with one mixed beam of repump beam and depump beam in previous optical arrangement, the main improvement here happens in the addition of another mixed beam in counter-propagation. The detail optical arrangement is described below. The Rb and Cs repump beams are combined together by polarizing beam splitter 1 (PBS 1) and two half-wave plates and then are blocked by a black dot of 5 mm in diameter in the center of combined beams. The Rb and Cs depump beams are combined together by another PBS 2 and two waveplates, and then fill the black dot in the combined repump beams. We divide the mixed repump and depump beams into two beams by the third PBS 3 and one half-wave plate and then make them irradiate atomic region in the opposite directions, shown in Fig. 1(a). Note that each beam has both repump beam and depump beam. With this optical arrangement, we can easily adjust relative space position of the two atom clouds and finally have an excellent overlap in dark SPOT. Fig. 1(b) shows the relative space movement of Rb and Cs cold atomic clouds in dark SPOT along horizontal direction when we change the power ratio of two repump (also depump) beams after PBS 3. The special optical arrangement for repump and depump beams make us to have nearly 100% overlap of the two atomic clouds. Fig. 1(c) shows the formation and ionization scheme of metastable ground state RbCs molecules. The photoassociation laser is provided by a continuous wave tunable Ti:
3. Results and discussion
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Fig. 1. Experimental scheme. (a) Brief diagram of optical elements near vacuum chamber. (b) Space movement of Rb and Cs atom clouds. The overlap can be easily adjustable when we change the power ratio of repump (also depump) beams after PBS 3 (see text) in the nearly opposite directions, shown in (a). (c) Formation and detection process of ultracold metastable ground state molecule. The mixed Rb and Cs atoms produced in (a, b) are photoassociated to þ RbCs molecules in J ¼1, v¼ 8, ð4Þ0 state of ð2Þ3 Π electric state followed by spontaneous emission to a3 Σ ground state, which is ionized to molecular ion þ in ð1Þ2 Σ state by REMPI. The potential energy curves are based on the data in Refs. [33,34].
Fig. 2. Photoassociation spectrum of v¼8, ð4Þ0 of ð2Þ3 Π excited state RbCs molecules.
photon (s) are then ionized by another PI photon to atomic ions, which are detected by MCP. The profile of PI spectrum obtained here is consistent with that obtained by Gabbnnini et al. [23–25], where Stark effect arising from static electric field was not eliminated and PA laser was only locked to a normal Fabry–Pérot interferometer. They proposed that the intermediate states in ionization þ process belong to ð3Þ3 Π and ð4Þ3 Σ electronic states. However, they did not give detailed discussion as PI spectrum were not the topics of those papers. Here we ignore the specific intermediate state in REMPI process, consider the þ þ transition from a3 Σ ground state to ð1Þ2 Σ molecular ion state when PA laser is locked at J¼1, v¼8, ð2Þ3 Π 0 rovibrational excited state. We use LEVEL program 8.0 [38] to calculate the wavefunctions and energies of vibrational states for the excited state, ground state, and molecular ion state based on the corresponding potential energy curves, which are taken from Refs. [33,34]. With the help of vibrational wavefunctions, we can further calculate the transition
probabilities between vibrational states of different potential energy curves. Fig. 4 shows the calculated transition probabilities from the v¼8, ð2Þ3 Π 0 excited PA state to the v¼0–29 vibrational þ states of a3 Σ state. These probabilities correspond to initial þ population distribution of different vibrational states on a3 Σ electronic state. It shows that ground state molecule population mainly distribute in the lowest decades vibrational states. þ We calculate transition probability from a3 Σ state distributþ ing in the range of v¼ 0 and v¼29 states to ð1Þ2 Σ molecular ion state by multiplying the initial population distribution. It needs to be noted that the ionization process contains two photons, the transition frequency between ground state to molecular ion state is two times larger than the value of dye laser frequency used in the experiment. The vibrational þ quantum numbers of ð1Þ2 Σ molecular ion state cover v¼21–74 in the scanning range of dye laser in Fig. 3. The data of PI spectrum and transition probability are available in supplemental files. Fig. 5(a) shows a small portion of Fig. 3(a) while Fig. 5(b) þ shows the corresponding transition probabilities from a3 Σ 2 þ state distributing in the range of v¼0–29 states to ð1Þ Σ molecular ion state. To compare with PI spectrum, transition þ þ frequency from a3 Σ state to ð1Þ2 Σ molecular ion state has been divided by number 2. We enlarge PI spectrum in this range for that the space between peaks is relatively larger, thus is favorable for spectrum analysis. The red solid line in Fig. 5(b) is smoothing results of the probability with point number of 30, which is the same as the number of vibrational states in ground state we have calculated. The smoothing results have been multiplied by 3 for the better comparison. For the nine peaks in Fig. 5(b), the corresponding transition final states (molecular ion state) are v¼24,…,33, which are shown on the top of Fig. 5(a). Take the first peak as an
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þ
Fig. 3. (a) Photoionization spectrum of a3 Σ ground state RbCs molecules when PA laser is locked at J ¼1 rotational state in Fig. 2. (b) Photoionization spectrum of Rb and Cs atoms in dark SPOT. The resonant transition lines are shown in the corresponding peaks, which agree with the dips of molecule photoionization spectrum in (a). The number 2 in denominator means that the dye laser frequency agrees with the transition frequency over 2.
Fig. 4. The calculated distribution probability of metastable ground state molecules by spontaneous decay when photoassociation laser frequency is locked at J¼ 1 rotational state in Fig. 2(a).
example, the ratio of transition probability to v¼24 and 25 þ states from a3 Σ ground state are 33.3% and 44.3%, respectively. The sum of transition probabilities to all other vibrational states is left 22.4%. The ratio for other cases is similar and can be obtained from supplement files if readers are interested. Comparing the measurement and calculated results, it shows that half parts of peaks in PI spectrum agree with calculated probability. Regards to the other half parts of peaks, we attribute this disparity to the complexity of PA state. There are strong mixtures between (4)0 and (6)1 states [24], which may affect the distribution of ground state molecules. In addition, the PA state may decay to high vibrational levels of singlet state via a multi-step process, from which the RbCs molecules can be ionized to RbCs þ by similar two-photon ionization process, or decay to low vibrational levels which are ionized to ions through absorption bands at 717 nm [39]. It is somewhat difficult to clarify this ionization scheme and
Fig. 5. (a) A portion of PI spectrum with relative clear peaks, shown in þ Fig. 3(a). (b) The corresponding transition probabilities from a3 Σ state þ distributing in the range of v¼ 0–29 states to ð1Þ2 Σ molecular ion state, mainly distributing in the range of v¼ 24–33 states. The red solid line is smoothing results with point number of 30 and magnify 3 times for the better comparison. The corresponding transition final state (molecular ion state) are shown on the top of (a). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
more comprehensive theory will be implemented in the future. 4. Conclusion To conclude, we have investigated the photoionization spectrum of metastable ground state molecules formed by
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spontaneous decay from J ¼1, v ¼8 rovibrational level of ð2Þ3 Π 0 short range excited state. Based on the available potential energy curves, we calculate energies of vibrational states for excited PA state, metastable ground state, and molecular ion state. Then we calculate the distribution of metastable ground state molecules and the transition þ probability from a3 Σ state distributing in the range of þ v ¼0 and v ¼29 states to ð1Þ2 Σ molecular ion state. An enlarged view of PI spectrum containing v0 ¼ 24–33 vibrational states of molecular ion is shown and half of peaks of PI spectrum agree with theoretical calculations. The PI spectrum analysis is meaningful for understanding population distribution of metastable ground state molecules and is also illuminating for other states, such as singlet ground state molecules, or other molecular PI spectrum. Future experiment will investigate the PI spectrum of singlet ground state molecules produced by the same intermediate excited state and STIRAP transfer to absolute rovibronic ground state molecules from nearly quantum degenerate atoms in optical dipole trap.
Acknowledgment The work was supported by the 973 Program (No. 2012CB921603), 863 Program (No. 2011AA010801), Natural Science Foundation of China (Nos. 61275209, 11304189, 61378015 and 11434007), NSFC Project for Excellent Research Team (No. 61121064), PCSIRT (No. IRT13076), the talent program of Shanxi and the NSF of Shanxi, China (No. 2014021004). Appendix A. Supplementary data Supplementary data associated with this paper can be found in the online version at http://dx.doi.org/10.1016/j. jqsrt.2015.07.008.
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