Creation of cold nitric oxide by extraction of the cold fraction of a thermal distribution Free

Cold-molecule physics applies the extra degrees of freedom of a molecule to the spectrum of topics at the forefront of cold and ultracold physics.¹ Polar molecules may provide unique opportunities to study quantum degenerate systems with strong, anisotropic interactions.¹ Cold and ultracold molecules are a fertile ground for interdisciplinary research in physics and chemistry,^1,2 in, for example, the long-sought goal of complete coherent control of chemical reactions. The dipole moment, rotational structure, and lambda doublet states available to molecules can be used for quantum computation^3,4 and quantum memory systems.⁵ 

Molecules with ²Π ground states offer great promise for the study of new physics. Light ²Π molecules such as OH, NO, NS, CH, may play a role in astrophysical observations of the time-variation of fundamental constants^6,7 and are important components of interstellar medium.⁸ Heavier molecules such as PbF(²Π) are important for their sensitivity to P-odd T-even (anapole moment) and P-odd T-odd (anapole moment and electric dipole moment) effects.^9–12 The power of using molecules in general for precision measurement was dramatically demonstrated by improvement of the limit on the electric dipole moment of the electron by an order of magnitude.¹³ 

Because progress in cold-molecule science has been slowed by the difficulty of initial preparation of the samples, significant resources have been devoted to the task of cold molecule creation. These methods fall into two primary categories: creation of cold gases from warmer samples of molecules and indirect formation of cold molecules from precooled atoms (photoassociation). The latter method relies on atomic cooling techniques, such as laser cooling. Many ²Π molecules of interest are not the photoassociation products of atoms that are easily laser cooled. A wide variety of methods have been employed to create cold gases directly,^1,14 including extracting the cold fraction from a warmer gas. The principle behind extraction as a method of producing samples of cold gases is that at any instant there exists a cold gas within the tail of the Maxwell-Boltzmann distribution of a warmer gas. The cold fraction must be extracted on a time scale small compared to the average collision time. Magnetic fields were used to extract the cold fraction from atomic sources^15,16 and molecular O₂,¹⁷ and electric fields have been used to demonstrate the technique for H₂CO,^18–20 ND₃,^18–26 water isotopologues,²⁷ and a number of other non-linear polar molecules.²⁴ In each case, guides were constructed that were bent at an angle. As the gas proceeded through the guide, the hottest atoms or molecules would not make it around the bend in the guide. Thus, the cold fraction would be transported to the output. The method of extraction is advantageous for its universality, applicable to any species with a significant magnetic or electric dipole moment.

Nitric oxide has a relatively small (≃0.15 D) electric dipole moment, but sufficient to be manipulated with laboratory capable electric fields. NO is chemically relevant and also very important in many biological systems and processes. The spectroscopy of NO is well known, and it has a high vapor pressure at low temperatures, which is advantageous for the extraction technique. In addition, NO ground-state molecules may be optically pumped between a ²Π_1/2 state that is non-magnetic (g ≈ 0.002) and a ²Π_3/2 state with g ≈ 2. This combination can be exploited to further cool the system through information (or entropy) cooling.^28,29

Previously, cold samples of NO in the X²Π_1/2 J = 15/2 state were created using molecular collisions^30,31 with densities of 10⁸ molecules cm⁻³ and temperatures of 400 mK. Subsequently, colder samples of 35 mK at 10⁶ molecules cm⁻³ densities were achieved.³² Cold samples of nitric oxide in the lowest vibrational level of the X²Π_3/2 state were formed using photodissociation with densities of 10⁷ molecules cm⁻³ and temperatures of 2 K.³³ Despite the relatively small dipole moment, Stark deceleration of NO in the X²Π_3/2 state successfully removed half the kinetic energy of a pulsed, supersonic beam.³⁴ 

We demonstrate the creation of a cold gas of NO by the extraction of the cold fraction from a thermal source. First, we describe an apparatus that cools a room temperature gas to 60-80 K by directly cooling the source tube with a cryogenic cooler. This gas is directed into a DC-electric hexapole guide. The output of the guide has a longitudinal speed distribution consistent with the measured temperature of the initial, cryogenically cooled gas. The speed distribution is measured using a field-stabilized Rydberg time-of-flight technique. In the presence of a constant electric field, molecules are excited to a superposition of Rydberg states that provide an enhanced lifetime sufficient to measure the low speeds of cold molecules. When a sphere is placed in the guide to block line-of-sight between the input and output of the guide, transmission is primarily limited to those in the lowest ro-vibrational states with sufficiently low kinetic energy to reflect from the walls of the guide. The one-dimensional speed distribution of the extracted gas fits a Maxwell-Boltzmann distribution with a temperature between 7 K and 20 K that varies with guide voltage and the temperature of the initial thermal source.

The apparatus is divided into two regions (a schematic is shown in Fig. 1). The molecular beam of NO is created in the first region, or source chamber. The NO is detected and the speed distribution is measured in the second region, or detection chamber. Between these two regions is an electric hexapole guide.^35,36 The NO travels through the guide into the detection region.

A 250 ℓ/s turbo pump, backed by a mechanical pump, provides initial pump-down for the system and helps provide vacuum for the source chamber. In combination with the turbo pump, a two stage cryogenic refrigerator with ultimate temperatures of 77 K and 4 K on the first and second stages provides an ultimate pressure of 2 × 10⁻⁹ Torr. We do not heat the system to improve vacuum. A gold-plated, copper cold shield is attached to the first stage to protect the coldest parts of system from background radiation heating. Inside the cold shield, a copper can, attached to the second stage of the cryogenic refrigerator, be cooled to a temperature as low as 16 K.

Nitric oxide enters the system through a 0.625 in. inner diameter stainless steel tube. This tube is connected to a needle valve external to the chamber, which controls the flow rate. A piece of teflon tubing is used as a thermal break just inside the chamber. A second steel tube attached to the teflon tube directs the NO into the copper can. A cooling block attached to the second stage of the refrigerator holds the NO source tube, causing the tube and the NO passing through it to be cooled (19 K minimum temperature). A small resistive heater and a resistive temperature sensor on the block provide temperature control of the NO through a LakeShore temperature controller feedback system. We typically run at temperatures between 60 K and 80 K, where there is appreciable vapor pressure of NO. The hexapole guide is attached to (but electrically insulated from) the side of the copper can opposite the NO source tube. Those particles with line-of-sight access to the hexapole guide entrance make it into the guide. The rest of the NO freezes to the walls of the copper can (maintained at 16-20 K). NO does not have appreciable vapor pressure below 40 K.

The electric hexapole guide that connects these two chambers is made from 3 mm solid copper rods 0.48 m in length.³⁷ They are polished and the ends are hemispherically shaped to prevent sparking. The wires are held in their hexapole orientation by several ceramic disks. The center of each wire is 0.6 cm from the guide center, the spacing between each wire center is 0.627 cm, and the internal guide region has a diameter of 0.820 cm. This configuration creates a cylindrically symmetric electric field about the guide axis. A voltage is placed on each rod, with adjacent rods having voltages of opposite sign. The electric field is zero along the guide axis for all applied voltages.³⁸ The maximum field strength is 65 kV/cm with applied voltages of ±4.5 kV. The entire length of the hexapole is surrounded by the cold shield. Finally, the hexapole passes through a differentially pumped region, which keeps most of the background NO from reaching the detection chamber. A 270 ℓ/s ion pump provides vacuum for the detection chamber with ultimate pressures reaching 5 × 10⁻⁹ Torr.

Each rotational level of the X²Π_1/2 ground state is split into two closely spaced (∼0.01 cm⁻¹) levels due to Ω-doublet splitting. Molecules in the Ω-doublet state with higher energy, denoted by f, are low-field seeking, their energy increases with increasing electric field. Molecules in the lower energy state, denoted e, are high-field seeking, their energy decreases with increasing electric field. This Ω-doublet splitting increases with rotational quantum number, which lowers the shift in energy due to the electric field. This increased splitting also leads to a Hund’s case classification of intermediate (a)-(b) for intermediate rotational quanta. However, low rotational levels can be approximated as purely Hund’s case (a) and are described by the vibrational (v), total angular momentum excluding nuclear spin (J), and Ω-doubling (e/f) quantum numbers. The A²Σ_1/2 state has Hund’s case (b) classification. The levels are described by their vibrational, total angular momentum excluding nuclear spin, and total orbital angular momentum (N) quantum numbers. The bandwidth of the laser is large (1 cm⁻¹) compared to the hyperfine structure, so we may neglect nuclear spin.

When an electric field is present in the guide, low-field seeking molecules are guided when the molecule’s transverse kinetic energy is smaller than the Stark interaction energy. Molecules without line-of-sight trajectories to the detector that do not satisfy this condition leave the guide. This increases the number of low-field seeking molecules that reach the detection region, while decreasing the number of high-field seeking molecules.

The molecules are detected by resonantly enhanced multi-photon ionization (REMPI) using two pulsed dye lasers (Lambda-Physik) pumped by a 10 Hz Nd:YAG laser (Continuum Surelite, 10 ns pulse width) at 532 nm (Fig. 2). The 678 nm output of the first dye laser is doubled and then tripled using Potassium Dihydrogen Phosphate (KDP) and Beta Barium Borate (BBO) crystals, respectively. This creates laser radiation in the 226-227 nm range. The 654 nm output of the second laser is doubled to 326-329 nm using another BBO crystal. The two beams are then made collinear, passed through a cylindrical lens, and directed through the chamber perpendicular to the molecular beam. The cylindrical lens focuses the beam to 200 μm along the molecular beam direction. A vertical beam radius (e⁻² point) of 1.5 mm intersects nearly all of the output of the guide. The 226 nm laser excites transitions in the |X²Π_1/2, v″ = 0〉 → |A²Σ_1/2, v′ = 0〉 band, where v″ and v′ are the vibrational quantum numbers for the ground and excited states, respectively. The 327 nm laser ionizes the NO molecules from the excited state. A pulsed electric field accelerates the ions towards a Burle microchannel plate, time-of-flight detector (TOF) where the ion current is recorded.

Spectroscopy on the output of the guide using REMPI shows enhancement of molecules in certain quantum states and suppression in others. Figure 3 shows ion counts observed as a function of the frequency of the first photon of the REMPI process. Spectra with the guide voltage set to ±4.5 kV and 0 kV are shown. The allowed transitions from the two lowest rovibrational states, J = 1/2 and 3/2 (those with the largest Stark effects), are calculated theoretically^39,40 and identified in the figure. Transitions from states of f quantum number (low field seeking states) show an increase in the number of ions detected. Transitions from states of e quantum number (high field seeking states) show a decrease in the number of ions detected. The enhancement is the result of a greater number of low-field-seeking molecules reaching the detection region due to guiding, and the suppression is due to the high-field seeking molecules being removed from the molecular beam by the presence of the guide field. (In this figure, there is no observed change in the allowed transition from the (J = 3/2, e) ground state. Several similar spectra were taken, and a decrease has been seen in other scans as there are fluctuations from run to run.⁴¹)

In typical TOF experiments, the spatial distribution of particles is marked at some initial time and allowed to expand. A measurement of the position distribution of the molecules at a later time is a measurement of the initial speed distribution of the sample, from which the temperature can be extracted. Because the numbers of cold molecules are low, we detect ions, which can have nearly unit efficiency. However, since the molecules exit the guide with low velocities, if they are ionized and allowed to expand, stray fields in our apparatus deflect the ballistic trajectories and introduce prohibitively large systematic error in the TOF measurement.

To avoid this common problem, Rydberg time-of-flight spectroscopy^42–45 is often used. In this procedure, particles are excited into a Rydberg state and allowed to expand while neutral. The particles are then field ionized and accelerated quickly toward a detector which records the position. The lifetime of the Rydberg state must be long compared to the time the gas is allowed to expand, which is common for atomic Rydberg states. Unfortunately for many molecules, Rydberg states are not long-lived. In NO, the Rydberg state lifetime is limited by predissociation,⁴⁶ which is highly dependent on the orbital angular momentum, ℓ of the electron of the Rydberg state.

Molecular Rydberg states with long lifetimes can be created by mixing the ℓ-states in an electric field.^47,48 This mixing is produced when a small static electric filed is applied to the system causing the overlap of the Stark manifolds of a number of the n states. This couples low-ℓ Rydberg states with high-ℓ states that have circular orbits that are less likely to interact with the ion core. This superposition, called field-stabilized Rydberg states, can be tailored to increase the lifetime to the microsecond time scale. This technique is commonly used in ZEKE spectroscopy.⁴⁹ 

Held et al.⁵⁰ used this idea to increase the lifetime of excited NO. First, the molecules are excited by a laser tuned to the |X²Π_1/2〉 → |A²Σ_1/2〉 transition. A second laser is tuned to a frequency that excites the molecules from the A²Σ_1/2 state to Rydberg states just below dissociation. While this process occurs, a small electric field (the stabilization pulse) is applied, mixing the ℓ-levels of the Rydberg states and increasing the lifetime.⁵⁰ The idea has also been applied to ion imaging of NO in photodissociation dynamics.⁵¹ 

Since the field-stabilized Rydberg states solve the problem of short lifetimes in the Rydberg TOF experiment, we call the technique Field-Stabilized Rydberg Time-Of-Flight (FSRTOF). A schematic of the FSRTOF apparatus is shown in Fig. 4(a), and the timing sequence is shown in Fig. 4(b). The design of this detector is similar in construction to the mass spectrometer built by Wiley and McLaren.⁵² There are three parallel disks (3 in. diameter, 1/16 in. thick) with central holes spaced 0.5 in. apart. The first two seen by the NO (entering from the right in Fig. 4(a)) have mesh screens to help keep field uniformity. The third is always kept at ground. The NO passes through the plates continuously.

The sequence starts with the second plate set to 100 mV for 100 ns. This is the stabilization pulse to mix Rydberg levels. After the stabilization pulse has been on 80 ns, we excite the NO using the two-photon pulse technique from Ref. 50. The two photons are created, overlapped, and focused as described in the REMPI measurement from Sec. III. The first photon comes from a laser tuned to the |J = 1/2, f〉 → |J = 1/2, N = 0〉 transition. It has a horizontal width (along the beam direction) of 200 μm, which is measured externally to the chamber and defines the dimensions of the sample of molecules, and is placed a distance 6.65 mm from the first disk. A second laser is set to 30581 cm⁻¹, a frequency that excites molecules into Rydberg states just below dissociation. The excited molecules evolve for a given time delay, T_delay, in which they typically drift longitudinally from 0.1 to 0.5 mm depending on their speed. After T_delay, 500 V is placed on the first disk, creating a field of 40 kV/m to field-ionize the molecules and accelerate them to the third, grounded plate. They pass through the plate into a Faraday cage and travel to the microchannel plate detector in approximately 1.4 μs. The detector records the time of arrival of the ions.

A Monte-Carlo simulation is used to fit the observed FSRTOF signals. The random selection of molecular speeds is weighted by a one-dimensional Maxwell-Boltzmann distribution. The initial size of the molecular cloud is given by the dimensions of the excitation laser. The location of the cloud at the moment of ionization is known by the arrival time of the peak of the distribution. We had previously measured the peak distribution arrival time as a function of position of the excitation lasers (without any time delay before ionization). This provides a mapping function for the FSRTOF apparatus that gives a location where the molecules were ionized as a function of the peak arrival time.⁴¹ Additional inputs to the model include the strength of the field ionization pulse and T_delay.

There are two fitting parameters. The first corresponds to the temperature of the Maxwell-Boltzmann speed probability distribution function, called T_fit. This is not a true temperature because the system is not expected to be in thermal equilibrium and is a measure of the average kinetic energy in only one dimension. Despite this, we find the data well represented by a Maxwell-Boltzmann distribution, consistent with previous results.¹⁶ The second is the magnitude of a small stray field. For a given temperature, 500 000 random speeds are selected based on the probability distribution function. Their trajectories are calculated by integrating Newton’s equations of motion. This procedure is repeated for a range of small stray fields. The sample signals are then compared to the experimental data and the final parameters are chosen based on a χ² analysis.

For a specific temperature, six delay times are used. Figure 5 shows the results of this measurement for four (of the six) delay times when the cooling block (Fig. 1) is kept at a temperature of 70 K. The simulations with the best fit to the data are also shown in the figure. Only data later than 1.42 μs were used in the fit. The features seen in the data at the earliest arrival times are excluded from the model. They are most likely a combination of autoionization or direct 1 + 1 ionization and imperfections in the system. We introduced a small electric field prior to ionization of the Rydberg molecules and were able to affect this artifact independently of the Rydberg molecule data. (When the system was upgraded for the next experiment (described below), the features did not reappear.) The χ² analysis for this system gave a fitted parameter of T_fit = 70 ± 3 K. We repeated the measurement when the cooling block was held at 77 K. The fit to those data gave T_fit = 77 ± 3 K. This represents the speed distribution in the lab frame, not the width of the molecular beam centered around a mean beam velocity. Theoretical calculations of the spectra in Fig. 3 incorporating population distribution of the rotational states as a function of temperature were matched to the experimental spectra and the temperatures were consistent with the results of FSRTOF and the measured temperature of the cooling block.

Previous methods of extraction use a curved guide.^15–27 A thermal source is injected into one end, and only the cold fraction is transported to the output as the guide cannot provide sufficient centripetal force for the hotter atoms. We present a different geometry to provide the extraction. We start with a straight guide, and then block line-of-sight between the input and the output of the guide by inserting a 3 mm diameter brass sphere in the geometrical center of the guide. Nearly all the molecules that make it to the output of the guide must be reflected off of the electric field walls and guided around the ball. Thus, it is analogous to a bent guide with a large radius of curvature. A guide with a larger radius of curvature will guide hotter atoms, thus extract a larger fraction of the total number of molecules. This is an advantage in that for the highest guide potentials, large signals will be observed. Lower final temperatures can be achieved by lowering the guide potential. This design has a construction advantage requiring only a straight guide.

We performed REMPI spectroscopy on the output of the guide with the ball blocking line-of-sight particles. The frequency tripled output of a pulsed dye laser is scanned, exciting transitions in the |X²Π_1/2, v″ = 0〉 → |A²Σ_1/2, v′ = 0〉 band. The output of a second pulsed dye laser is doubled and tuned to a frequency of 327 nm, which ionizes the NO molecules from the A state. Figure 6(a) shows ion counts observed as a function of the frequency of the first photon of the REMPI process. Similar to before, spectra with the guide voltage set to ±4.5 kV and 0 kV are shown, and the allowed transitions from the two lowest rovibrational states are labeled. A background is observed as we find the ball does not block all line-of-sight particles from the source. We identify the remainder of the transitions by matching the spectra to calculated spectroscopy of NO at different temperatures (77 K and 300 K). Figure 6(b) is the difference in ion counts with guide voltage on and off. There is clear signal from the guide in the lowest, J = 1/2 state. A signal from the J = 3/2 state is slightly above the noise. The largest feature corresponds to a frequency that excites molecules from both states.

To show that the detected molecules represent the extracted cold fraction of the beam, we perform FSRTOF on the output of the guide. Figure 7 shows the results of this measurement for four (of the six) delay times for a typical run with the guide on. The vertical scale is in arbitrary units and cannot be compared to data from Figure 5. In these data, two distributions are observed, which we predict are the extracted cold fraction and a small amount of the original distribution that made it through the guide. The high temperature distribution can be seen as the small secondary curve contributing to the enlarged tail at earlier flight times. With the guide off, only the small background is observed matching the small 77 K component of the distribution observed with the guide on. The thermal source is kept at a temperature of 77 K through control of the cooling block (Fig. 1). To simulate the output, we use the same model and approach as before, except the probability distribution of speeds consists of two Maxwell-Boltzmann distributions with different fitting temperatures. Since we have found that the guided output without the ball is well measured by the cooling block temperature, one of the model distribution temperatures is not a fitting parameter but set by the expected thermal temperature of the source.

We calculate a lower bound on the flux of extracted molecules from the total number of ion counts on the detector for a source temperature of 77 K and a guide voltage of 4.5 kV. We assume all the NO in the excitation volume are ionized and hit the detector, which have a known quantum efficiency. Integrating separately the two components from the fits in Figure 7, the integral of the colder distribution in each fit is between 89% and 91% of the total. Thus, assuming 90% of the detected ions are part of the extracted, cooler distribution, we estimate (3.8 ± 1.9) × 10⁵ cm⁻² s⁻¹ molecules exiting the guide in a single rovibrational state.

This fit is illustrated in Figure 7 for a source temperature of 77 K and a guide voltage of ±4.5 kV, and yields a fitting parameter T_fit for the extracted distribution of 18 ± 2 K. The simulation is also fit to the spatial distributions measured when the guide voltage is set at ±4.0 kV, ±3.5 kV, and ±2.5 kV at the 77 K source temperature. We perform a similar analysis to measure distributions at both 72 K and 82 K source temperatures. The results of this analysis are found in Table I. This shows that the system successfully extracts a cold fraction from the thermal source, and that the temperature of the resulting gas can be decreased by decreasing the guide voltage, though this does result in fewer particles in the sample. The transverse guiding potential varies between 50 and 100 mK, thus the transverse speeds will be much lower than the longitudinal speeds. Therefore, the numbers in Table I are conservative overestimates. The extracted gas will have an average thermal energy less than that of a gas in thermal equilibrium with the temperature equal to T_fit.

For an extraction technique, the total number of particles in the original sample limits the efficacy of the procedure. In the current apparatus, the end of the NO source tube is placed nearly 4 in. from the input of the guide. When we placed it closer, the NO source tube became too cold and the NO froze in the tube blocking further NO from escaping. A straightforward improvement is to have a self-heating NO source tube with a small current that can maintain the desired temperature over the entire length of the tube.⁵³ Simply being able to place the source tube inside the Stark guide will increase the initial flux over one order of magnitude. Simulations suggest that this will result in appreciable fluxes at temperatures ≃0.1 K.⁴⁰ At these temperatures, NO can be trapped in a permanent magnetic trap by optically pumping the molecules from the X²Π_1/2 into the X²Π_3/2 state.^40,54,55 Given that NO has a relatively weak electric dipole moment, the method will only be more effective with other ²Π systems.

We have demonstrated a continuous, state selective source of cold nitric oxide molecules. After pre-cooling the NO gas to 72-82 K, a molecular beam is inserted into a hexapole Stark guide. The speed distribution is measured by field-stabilized Rydberg time-of-flight, which is shown capable of measuring speed distributions of cold samples of molecules not amenable to standard Rydberg time-of-flight because of the short lifetime of molecular Rydberg states. The cold fraction is extracted from the thermal source by blocking line-of-sight between the input and the output of the guide. This ensures that most particles must reflect from the wall of the guide where the size of the potential barrier can limit the kinetic energy of the transmitted particles. We have shown that by changing the source temperature and electric field strength we can control the temperature of the gas of molecules exiting the guide.

This work is supported by the Office of Naval Research Contract No. N00014-02-1-0601.