† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 91536218, 11034002, 11274114, 11504112, and 11504318) and the National Basic Research Program of China (Grant No. 2011CB921602).
A scheme of surface manipulation and control of polar molecules is proposed, which combines three tools of electrostatic velocity filtering, bunching, and storing. In the scheme, a slow molecular beam is produced from an effusive beam by surface velocity filtering. Then the velocity spread of the slow molecular beam is compressed by a buncher consisting of a series of electrodes. Following that the molecular beam with a narrow velocity spread is stored in a storage ring. Using ND3 molecule as a tester, the feasibility of our scheme is analyzed theoretically and verified via numerical simulations that cover all three manipulation processes. The results show that cold molecular samples can be prepared from a thermal gas reservoir and stored in the storage ring with more than 10 round trips. Our combined scheme facilitates the production and manipulation of polar molecules, offering new opportunities for basic research and intriguing applications such as quantum information science and cold collisions.
Cold molecules is a fast-growing research area motivated by many fascinating possibilities in fundamental studies and applications like cold collisions[1] and precision measurements.[2] Various approaches have been demonstrated to obtain cold molecules, including buffer gas cooling,[3] electrostatic Stark deceleration,[4,5] Zeeman deceleration,[6] laser cooling,[7,8] photoassociation,[9] and so on. Among them, electrostatic velocity filtering is a simple method that allows for selecting slowly moving molecules from a thermal gas reservoir. This idea was first proposed in the 1950s,[10] however, it was not experimentally successful until 1999. In 1999, Ghaffari et al. obtained a slow lithium atomic beam from a gas reservoir by using a low-pass velocity filter made of permanent magnets.[11] In 2003, Rempe’s group successfully selected slow polar molecules out of a room-temperature reservoir via a bent electrostatic quadrupole.[12] In 2010, Bertsche et al. demonstrated a curved electrostatic hexapole[13] that can also be used to prepare slow polar molecules. The velocity-selected molecular beam has been applied to various experiments such as ion–molecule collisions[14] and cold molecule collisions.[15]
A cold molecular beam with a certain forward velocity can be confined in a storage ring, which permits the beam to repeatedly appear at certain times and positions. In 1997, Katz proposed a design of an electrostatic storage ring for polar molecules,[16] which was demonstrated by Crompvoets et al. in 2001.[17] Subsequently, a sectioned storage ring and a synchrotron for polar molecules were demonstrated,[18–20] which greatly increase the number of round trips of the beams. Most recently, we proposed a scheme of synchrotron allowing for controlling heavy polar molecules.[21]
In this paper, we present a combined scheme which integrates multiple manipulation tools on a substrate, including an electrostatic velocity filter, a buncher, and a storage ring. Compared to the existing manipulation tools for polar molecules, our design has the following advantages. (i) Our scheme includes both functions of production and manipulation of cold polar molecules; (ii) The scheme is based on a substrate. In other words, the cold molecules are produced and controlled in the vicinity of a substrate, which holds promising applications such as quantum computing science and the studies of molecule–surface interaction; (iii) The compact design permits them to integrate on a chip when scaling down the geometry size.
This paper is arranged as follows. Firstly, the design of multiple manipulation tools for polar molecules is introduced, and each function element is detailed one-by-one. Secondly, the feasibility of our scheme is analyzed theoretically and verified using the method of Monte–Carlo simulation with the sample molecule ND3. The main results and conclusions are given in the end.
Our design, including the electrostatic velocity filter, the buncher, and the storage ring, is shown in Fig.
An effusive beam is produced by a pulse valve and then is loaded into the velocity filter which allows for preparing a slow molecular beam in the vicinity of the surface of the substrate. Subsequently, the slow molecular beam is compressed in velocity space by the buncher and finally confined in the storage ring. The heights of the potential well minima in the three manipulation tools, which can be adjusted by changing the voltages applied on them, are almost the same. Therefore, the loading efficiency of molecules among the these parts can get to a maximum. The three manipulation tools are integrated together that ensures minimizing the loading loss among them. In the following sections, the details of each element will be given one-by-one. The test parameters of the scheme are listed in Table
The electric filter is formed by bending electrodes into quarter circles with a radius of curvature Rf. When the lower and upper cylindrical electrodes are respectively charged with proper positive voltages U1 and U2, an electrostatic guiding center (minimum of the electric field strength) can be formed for low-field-seeking (LFS) state molecules above the surface of the substrate. The analytic expression of the electric field in our scheme is difficult to obtain, therefore we turn to numerical calculations. When voltages U1 and U2 are respectively set as 22 kV and 30 kV, a guiding tube for polar molecules appears, with a height of 1.2 mm from the surface of the substrate, i.e., 0.7 mm above the surface of the lower cylindrical electrode, as shown in Fig.
In the presence of the electrostatic fields, the Stark potential for polar molecules is given by[22]
The buncher consists of an array of cylindrical electrodes that are half-embedded in the substrate, as shown in Fig.
By alternatively switching the two configurations in proper time, the molecular beams are bunched longitudinally. Thus the beam is kept together as a compact packet. The principle of bunching is in fact similar to that of the traditional Stark deceleration[25] with zero phase angle. During the bunching process, the molecules revolve in the phase space and get to a minimum of velocity (or space) spread at a certain time. Thus the velocity and space spread of the molecules can be controlled by adjusting the voltages applied on the electrodes and the number of the bunching stages. During the bunching process, the phase-space density remains constant according to the Liouville theorem.
Figure
The original molecular beam contains ∼ 4 × 106 ND3 molecules in the LFS state |J, KM⟩ = |1, −1⟩. The longitudinal velocity of the input molecular beam centers around υc = 120 m·s−1 with a velocity spread (full width at half maximum, FWHM) of 130 m·s−1 and the transverse velocity spread is 30 m·s−1 in both x and y directions. These parameters are realistic from Refs. [26] and [27]. The corresponding longitudinal and transverse temperatures are respectively 7.4 K and 393 mK in the moving frame, as obtained from the formula m (Δυ2/(8 ln 2kB,[28] where kB is the Boltzmann constant. The space spreads are 20 mm and 1 mm in the longitudinal and transverse directions, respectively. Both the position and velocity spreads are Gaussian distributions. The geometrical parameters of the three elements are listed in Table
The Monte Carlo simulations start from the bend velocity filter. After being filtered, the center velocity of the beam is reduced to ∼ 80 m·s−1, as shown in Fig.
Following the electric filter, the resulting beam is coupled into the buncher, where the longitudinal velocity of the synchronous molecule is set to 100 m·s−1, slightly higher than the most probable velocity. After a bunching of 20 stages, the longitudinal velocity spread is greatly reduced from 73 m·s−1 to 8.9 m·s−1, as shown in Fig.
Immediately after being bunched, the molecular packet is loaded into the storage ring and takes round trips. The TOF spectrum of the molecular packet revolved in the storage ring is indicated in Fig.
A scheme integrating three manipulation tools, i.e., an electrostatic surface filter, a buncher, and a storage ring, is proposed and analyzed theoretically. Using the test molecule ND3, Monte–Carlo simulations that cover all three elements are carried out to verify the possibility of our scheme. Our calculation results show that the velocity spread of an effusive beam can be greatly reduced from 130 m·s−1 to 5.5 m·s−1 after being filtered and bunched, which permits the molecular packet to make 10 round trips in our storage ring. These results show that it is effective to produce and control polar molecules in our scheme. Additionally, our scheme can offer a robust force and open optical access, which allows for preparing more cold molecules and facilitates detecting and manipulating molecules in the structure.
Our scheme can find many applications in molecular beam experiments, such as cold collisions,[1] cold chemistry,[30] high-resolution spectroscopy,[31] precision measurements,[2] and quantum optics.[32–34] The trap height above the surface of the substrate can be adjusted easily, which holds promising applications such as quantum computing science and the studies of molecule–surface interaction.
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