Rydberg-Stark deceleration of atoms and molecules

Abstract

The large electric dipole moments associated with highly excited Rydberg states of atoms and molecules make gas-phase samples in these states very well suited to deceleration and trapping using inhomogeneous electric fields. The methods of Rydberg-Stark deceleration with which this can be achieved are reviewed here. Using these techniques, the longitudinal motion of beams of atoms and molecules moving at speeds as high as 2500 m/s have been manipulated, with changes in kinetic energy of up to |Δ E _kin|=1.3×10^-20 J (|Δ E _kin|/e=80 meV or |Δ E _kin|/h c=650 cm ^-1) achieved, while decelerated and trapped samples with number densities of 10⁶- 10⁷ cm ^-3 and translational temperatures of ∼150 mK have been prepared. Applications of these samples in areas of research at the interface between physics and physical chemistry are discussed.

Keywords: Cold atoms and molecules; Rydberg states of atoms and molecules; Stark deceleration; Stark effect.

Fig. 1

Rydberg states of atoms and molecules. Schematic diagram of series of Rydberg states in the hydrogen atom (H), in other non-hydrogenic atoms (X), and in molecules (AB)

Fig. 2

High-resolution millimeter-wave spectra of Kr. Millimeter-wave spectra of the 77d[3/2](J ^′=1)→93p[3/2](J=1) transition in Kr recorded following interaction times between the atoms and the millimeter-wave field of τ=3, 6 and 18 μs as indicated. The corresponding transition line-widths are 350, 180 and 60 kHz, respectively. From [6] with permission

Fig. 3

Long-range Rydberg molecules. a and (b) the scattering process involving an electron in a diffuse Rydberg orbital and a ground state Rb atom which gives rise to sets of bound molecular eigenstates. c Experimentally measured transitions to the lowest vibrational states of long-range Rb₂ Rydberg molecules in the vicinity of the 37s (bottom), 36s (middle) and 35s (top) single-atom Rydberg states. From [67] with permission

Fig. 4

Coupling Rydberg atoms to microwave circuits. a Photograph of a coplanar microwave waveguide with the position of a sample of Rydberg atoms, when probed by a pulsed microwave field propagating along the transmission line, indicated schematically by the red shaded region. b-c Rabi oscillations observed in an ensemble of Rydberg atoms coupled to the microwave field surrounding the waveguide for microwave powers of 4 μW and 10 μW at the source. d-e Fourier transforms of (b) and (c). From [39]

Fig. 5

Spectra of Rydberg states of positronium. a Two-colour two-photon excitation spectrum of Rydberg states of Ps with values of n from 9 up to the ionisation limit. States with values of n>17 are detected when they annihilate after ionisation at a wire grid close to the photoexcitation region (early annihilation). States with values of n<17 pass through this grid and are detected when they annihilate at the walls of the vacuum chamber (late annihilation). b When photoexcitation is carried out in the presence of an electric field of 1.9 kV/cm individual Rydberg-Stark states can be selectively prepared. From [82]

Fig. 6

The Stark effect in Rydberg states of the H atom. a Dependence of the energies of m=0 Stark states with values of n from 7 to 14 on the strength of the electric field. b Electron probability density in a plane containing the electric field axis for n=8 Stark states with k=−7,−1,+1 and +7. After [90]

Fig. 7

Fluorescence lifetimes of Rydberg states of the H atom. a Fluorescence lifetimes of field-free states of the H atom with n=30 and 50, for each allowed value of ℓ. b Fluorescence lifetimes of |m|=0,1 and 2 Rydberg-Stark states with n=30 and 50, and each allowed value of k

Fig. 8

The Stark effect in non-hydrogenic atoms. Energy level diagrams depicting the Stark effect in n=15 Rydberg states of Li with a m=0, b |m|=1, and c |m|=2, and d n=15 Rydberg states of the H atom with m=0

Fig. 9

The Stark effect in Rydberg states of H₂. Calculated Stark maps for para H₂. N ⁺=0 states are indicated in black, N ⁺=2 states are indicated red, and N ⁺=4 states are indicated in blue. a |M _J|=0, b |M _J|=1, and c |M _J|=3. From [98]

Fig. 10

Thermal photon occupation numbers. Mean blackbody photon occupation number (a) at frequencies up to 300 GHz (10 cm ⁻¹) and (b) at frequencies up to 5000 GHz (160 cm ⁻¹), for blackbody temperatures of 300 K, 125 K, 10 K and 4 K

Fig. 11

Transverse deflection of beams of Kr Rydberg atoms. a Schematic diagram of the experimental setup, including the inhomogeneous dipolar electric field distribution above the two cylindrical metallic rods, used to transversely deflect beams of Kr atoms. b Stark map for Rydberg states with values of n close to 18 in Kr. The Stark states labelled A to F on the righthand side of the figure were selectively excited and subjected to the deflection fields. c Experimentally recorded (Expt.) and calculated (Calc.) images of beams of atoms after deflection. From [110] with permission

Fig. 12

Acceleration and deceleration of beams of H₂. Time-of-flight distributions of H₂ molecules in extreme outer low-field-seeking (upper trace) and high-field-seeking (lower trace) Rydberg-Stark states for which n=17, after exiting a time-independent inhomogeneous electric field. From [99] with permission

Fig. 13

Acceleration and deceleration of beams of Ar atoms in time-dependent electric fields. a Electrode configuration used in the acceleration/deceleration of Ar Rydberg atoms using time-dependent inhomogeneous electric fields. b Time dependence of the potentials applied to electrodes 3 and 4 in (a) for acceleration/deceleration. c Experimentally recorded time-of-flight distributions demonstrating the acceleration (left-hand red dataset), deceleration (right-hand blue dataset) of high-field-seeking (HFS) and low-field-seeking (LFS) n=16 Rydberg-Stark states, respectively. The central black dataset represents the time-of-flight distribution of the undecelerated Rydberg atom beam. From [114] with permission

Fig. 14

Electrode configuration of a Rydberg atom mirror. a–c Schematic diagrams of the set of metallic electrodes used to reflect beams of H Rydberg atoms in a normal incidence mirror. The electric potentials and corresponding field distributions at the time of (a) photoexcitation, (b) deceleration/reflection, and (c) detection are displayed. c Time-dependence of the electric potentials applied to each mirror electrode. From [115] with permission

Fig. 15

Measurements of reflected H Rydberg atoms. a Individual H ⁺ time of flight distributions recorded after pulsed electric field ionisation of atoms located between electrodes 1 to 4 in Fig. 14(a) at the times indicated by the dashed vertical lines. Positive-going datasets were recorded with the mirror off, while the negative-going, inverted datasets, were recorded with the mirror on. b Dependence of the mean longitudinal position of the cloud of Rydberg atoms, with respect to the position of photoexcitation, on the time delay before pulsed electric field ionisation as extracted from the data in (a) with the mirror off (open red circles), and on (filled black circles). From [116] and [150] with permission

Fig. 16

Three-dimensional electrostatic trap. a Schematic diagram of a single-stage Rydberg-Stark decelerator and three-dimensional electrostatic trap. b and (c) electric field distributions in the yz and xz planes at the center of the trap with potentials of |V _1,2,3,4|=20 V and |V _5,6|=55 V. The contour lines are spaced by 10 V/cm with the center-most corresponding to a field of 20 V/cm. The color bar indicating the field strength in (c) also holds for (b). From [118]

Fig. 17

Time-dependent deceleration and trapping potentials. Time dependence of the electric potentials applied to electrodes 1–4 in Fig. 16(a). a Ionisation pulses applied to electrodes 1 and 2 to detect the trapped Rydberg atoms. b Exponentially decaying deceleration potentials applied to electrodes 3 and 4. The horizontal axis represents the time after photoexcitation

Fig. 18

Acceleration and relative position of atoms during deceleration and trap loading. a Acceleration, and (b) relative longitudinal position in the z dimension with respect to the final position of the trap minimum, of H atoms in the |n,k〉=|30,25〉 state for which the time-dependence of the deceleration potentials was optimised. The origin of the horizontal axis is the activation time of the deceleration potentials

Fig. 19

Decay of H Rydberg atoms from on-axis and off-axis electrostatic traps. On-axis (open circles) and off-axis (filled circles) decay of H atoms initially prepared in n=30 Rydberg-Stark states from traps operated at 300 K. The solid lines are single-exponential functions fitted to the experimental data beyond 200 μs. From [105]

Fig. 20

Imaging the transverse motion of H Rydberg atoms in an on-axis electrostatic trap. ‘Breathing’ motion of a trapped ensemble of H Rydberg atoms recorded by imaging the spatial distribution of H ⁺ ions detected at the MCP for selected times after pulsed electric field ionisation. a Experimentally recorded data, and (b) calculated images. From [118]

Fig. 21

Off-axis electrostatic trap. a Schematic diagram of the Rydberg-Stark decelerator and off-axis electrostatic trap (not to scale). In this figure, the end-cap electrodes (E5 and E6, and E9 and E10) which close off the on-axis and off-axis quadrupole traps formed between electrodes E1–E4 and E2, E4, E7 and E8 in the y dimension [see Fig. 16(a)] are omitted for clarity. b The sequence of electric potentials applied to the six principal electrodes of the device for deceleration and off-axis trapping. The time on the horizontal axes in (b) is displayed with respect to the time of photoexcitation. From [120]

Fig. 22

Electric field distributions in the off-axis decelerator and trap. Electric field distributions in the yz plane of the off-axis trap (a) at the time of photoexcitation and after completion of the trapping process, (b) in the initial phase of on-axis deceleration, (c) during the 90° deflection process, and (d) in the final deceleration phase. The lines of constant electric field range in (a) from 10 to 100 V/cm in steps of 10 V/cm, and (b–d) from 20 to 200 V/cm in steps of 20 V/cm. The red shaded circles indicate the center of the Rydberg atom cloud at each time. From [105]

Fig. 23

Blackbody temperature, and isotope dependence of trap decay. a Temperature dependence of the decay of trapped H atoms initially prepared in n=32 Rydberg-Stark states. Experiments were performed at 300 K (open squares), 125 K (black filled circles), and 11 K (open circles). From [151]. b Decay of H (open circles) and D (filled circles) Rydberg atoms, initially prepared in Stark states for which n=30, from an off-axis electrostatic trap operated at 125 K. From [120]

Fig. 24

Evolution of Rydberg state populations in a 125 K environment. a H ⁺ ion time-of-flight distributions recorded following ramped electric field ionisation 50 μs after trapping H Rydberg atoms initially prepared in Stark states with values of n from 30 to 37. b The time-dependent ionisation potential applied to electrodes 2 and 7 in Fig. 21(a) to ionise the trapped atoms. c Evolution of the ion time-of-flight distribution for atoms initially prepared in states for which n=30 as the trapping time is increased in an environment cooled to 125 K. The vertical red bars indicate the ion arrival times for states with consecutive values of n as determined from (a). From [152]

Fig. 25

Trapping H₂ molecules in selected Rydberg-Stark states. (a,i) n=22, |M _J|=3 Stark spectrum of H₂ recorded in an electric field of 278 V/cm with detection after a time delay of 3 μs. (ii,iii) Spectra of low-field-seeking k=10−18, n=22, |M _J|=3 Stark states of H₂ detected after a trapping time of 50 μs with deceleration potentials of (ii) ±1.7 kV and (iii) ±2.3 kV. (b,ii) and (b,iii) Calculated spectra obtained following numerical simulations of particle trajectories for deceleration potentials of (ii) ±1.7 kV, and (iii) ±2.3 kV. c Calculated |M _J|=3 Stark structure in the vicinity of n=22 in H₂. The thick lines indicate the range of maximum electric-field strength experienced by molecules during deceleration with potentials of (ii) ±1.7 kV, and (iii) ±2.3 kV. From [98]

Fig. 26

Decay of trapped H₂ molecules. Measurements of the number of H${}_2^{+}$ ions detected following pulsed electric field ionisation of H₂ molecules from an on-axis electrostatic trap in a room temperature environment. Dataset A (B) was recorded with the pulsed valve operated at a stagnation pressure of 4.0 bar (1.75 bar). From [101]

Fig. 27

A surface-electrode Rydberg-Stark decelerator. a Schematic diagram of a surface-electrode-based Rydberg-Stark decelerator and surrounding photoexcitation and electric field ionisation regions. b Oscillating potentials applied to the 11 electrodes of the decelerator in (a) for the deceleration of H atoms from v _i=760 m/s to v _f=300 m/s. From [136]

Fig. 28

Electric field distributions in a surface-electrode Rydberg-Stark decelerator. Electric-field distribution in (a) the xz-plane containing the trap minima, and (b) the x=0 plane in a surface-electrode Rydberg-Stark decelerator. The positions of the decelerator electrodes are indicated on the horizontal axis in (b). The 0 V plate is located at y=−0.75 mm. From [136]

Fig. 29

Potential energy distributions in the moving frame of reference associated with an electric field minimum in a surface-electrode Rydberg-Stark decelerator. Potential energy distributions in the yz-plane at the mid-point of a surface-electrode Rydberg-Stark decelerator in the x-dimension surrounding a moving electric field minimum for accelerations of 0, −5×10⁵, −5×10⁶ and −5×10⁷ m/s². The contour lines are spaced by E/k _B=1 K beginning at 1 K. Cases for which H atoms in (a–d) |n,k〉=|33,26〉, and (e–h) |50,40〉 states are displayed. As are those in (i) and (j) for Xe atoms in the |50,40〉 state

Fig. 30

Acceleration and deceleration of H atoms in a surface-electrode Rydberg-Stark decelerator. a Experimental, and (b) calculated H-atom time-of-flight distributions demonstrating acceleration/deceleration of atoms in states for which n=31 from v _i=760 m/s to v _f=1 200, 1 000, 600, 450, 300 and 200 m/s. From [136]

Fig. 31

Trapping stationary samples of He atoms in a surface-electrode Rydberg-Stark decelerator. He Rydberg atom time-of-flight distributions after deceleration, trapping, and re-acceleration in a surface-electrode decelerator. The states initially prepared at photoexcitation were those for which |n,k,m〉=|30,23,0〉. The dashed vertical lines indicate the He atom detection times after trapping stationary samples for times ranging from 0 to 50 μs. The dependence of the integrated time-of-flight signal on the trapping time is indicated in the inset, together with the decay rate associated fluorescence alone. From [137] with permission

Fig. 32

Surface-electrode decelerator and deflector for Rydberg atoms and molecules. Schematic diagram of the surface-electrode decelerator and deflector used to manipulate beams of H₂ molecules in high Rydberg states. (i) The Rydberg state photoexcitation region is located between two parallel metal plates. (ii) The curved surface-electrode decelerator permitted controlled transport and deflection of the H₂ molecules away from their initial axis of propagation. (iii) Deflected and undeflected molecules were directly imaged on a MCP detector. From [138] with permission

Fig. 33

A transmission-line Rydberg-Stark decelerator. a Schematic diagram of a transmission-line decelerator for Rydberg atoms and molecules. Typical electric field distributions in (b) the transverse xy-plane, and (c) the longitudinal yz-plane employed for trapping, transport and deceleration are also displayed. From [87]

Fig. 34

Guiding, accelerating and decelerating He atoms in a transmission-line decelerator. a He atom time-of-flight distributions recorded after passing through a transmission-line decelerator (i) when the device was off, and (ii) after velocity selection and guiding at a range of longitudinal speeds as indicated. b Time-of-flight distributions recorded following acceleration/deceleration of atoms travelling with an initial longitudinal speed of 1950 m/s. From [87]