Towards trapping of Rydberg Ps

Atoms and molecules in high Rydberg states can possess large electric dipole moments which can be exploited to control their motion using external electric fields. Ever since the demonstration of deflection of Rydberg Kr atoms using electric fields (https://doi.org/10.1088/0953-4075/34/3/319), the field of atom optics has been widely investigated. Different techniques such as decelerators [EPJ Techniques and Instrumentation (2016) 3:2], mirrors [Phys. Rev. Lett. 97, 033002 (2006)], and traps [Phys. Rev. Lett. 100, 043001 (2008)] have been developed, however applications to positronium (Ps) are relatively recent. Only a handful of Ps atom optics experiments have been performed to date [Phys. Rev. Lett. 117, 073202 (2016) , Phys. Rev. A 95, 053409 (2017) , Phys. Rev. Lett. 119, 053201 (2017)]. Several Ps experiments can benefit from use of a cold Ps source but, due to the low mass of Ps, speeds are often on the order of 100 km/s when produced in targets like mesoporous silica. Also, using mesoporous silica, the Ps angular distribution during emission is broad and if a well collimated beam is required, significant loss in Ps number is unavoidable. The use of time-varying electric fields generated by a multi-ring structure can offer a solution to these limitations by capturing more emitted Ps and allowing manipulation via their electric dipole moments. Recently, we have developed a multi-ring structure which has been implemented to guide Rydberg Ps atoms using inhomogeneous electric fields, and, in principle, can also be used to decelerate and trap Ps.

The experimental set-up of the target and electrostatic guide including the excitation lasers and the gamma-ray detectors is shown in Figure 1. The Ps producing target is labelled T and the 11 electrodes of the guide are labelled 1, 2, 3,…, 11. Ground state Ps atoms, produced from the silica target, are excited to the n=13 Rydberg level in a two step process by the UV (1S –>2P) and IR (2P–>nD/nS) lasers in the region between T and electrode 1 (E1). Once excited to Rydberg states, Ps atoms have lifetimes on the order of μs, significantly longer than the triplet ground state lifetime of 142 ns. A 500 V/cm electric field, generated by biasing T and E1, Stark splits the Rydberg spectrum [Phys. Rev. Lett. 114, 173001 (2015)], enabling us to select specific states in the Stark manifold by tuning the IR laser wavelength. States selected with positive Stark shift(shorter wavelengths) are called low field seekers (LFS), because of their property to move toward regions of low field. States selected with negative Stark shift (longer wavelengths) are called high field seekers (HFS), because of their property to move toward regions of high field. Any atoms that are able to traverse the guide, LFS or HFS, can then be detected by detectors D2, D3, D4, and D5.

Schematic(2ndVersion)
Figure 1: Schematic of the Ps production and excitation chamber. Inset shows the target electrode, T, and guide assembly comprising of 11 electrodes.
guideoff
Figure 2: Simulated trajectories of atoms in HFS states (red solid lines) and LFS states (white solid lines) of the n=13 Stark manifold, with guide “off” (a) & (b) and “on” (c) & (d)

According to our simulations, see Figure 2, when the guide is not in operation (all electrodes grounded at 0V), the diverging cloud of Ps atoms from the target do not experience any external forces as expected, and therefore annihilate after colliding against the guide electrodes, with only a few forward collimated atoms reaching the end of the guide. If we apply a voltage to alternate electrodes (3,5,7 etc.), this turns the guide on. In this case the HFS states are deflected toward regions of high electric fields (i.e. away from the axis of the guide) while the LFS states are confined axially and transported along the length of the guide. These LFS atoms diverge after exiting the guide and some annihilate due to collisions with the surrounding vacuum chamber. Detectors D2, D3, D4, and D5, as shown in Figure 1, are able to record these annihilation events as time of flight (TOF) spectra, the results of which are shown in figure 3 below.

LFSvsHFS2
Figure 3: TOF spectra/annihilation events seen by detectors D2, D3, D4, and D5 for Ps atoms in (a) LFS and (b) HFS states with guide both on and off.

Neither the LFS states nor the HFS are detected at the end of the guide when the guide is off but an increased count rate is seen when both the guide is on and the IR laser is tuned to excite atoms to the LFS states.

To implement this device as a trap, we only have to reconfigure the voltages applied to the electrodes. For guiding, the odd numbered electrodes of the guide have a voltage applied (-4 kV) while the even numbered electrodes are kept at ground potential (0 V). If a positive voltage of order +1 kV is applied to E2 and E4 while E3 is at a potential of -4kV, then a region of electric field minimum is created in the centre of E3 (the voltages applied to the electrodes are based on the choice of n due to the field ionisation limit). Once the atoms have entered the trap, the LFS atoms should be confined in this region until the voltage applied to E4 is lowered,  opening the trap gate for the atoms to be guided towards the detectors. If atoms are trapped and guided out, then the TOF spectra, like in Figure 3(a), is expected to show a peak in events but occurring with a delay consistent with the length of trapping.

In pursuit of cold Ps

Experiments involving positronium (Ps), such as laser excitation for Rydberg state production, precision spectroscopy and positronium chemistry can benefit from a slow Ps source. The technical word for slow is cold. As the mass of positronium is twice the mass of an electron, even room temperature Ps have speeds on the order of 100 km/s. In comparison, atomic beams produced from supersonic jets have speeds of roughly 2 km/s. Atom optics techniques such a decelerating the Ps with electric fields to slow down the atoms may be possible, but at the cost of loss in intensity. An ideal alternative would be to fabricate a target that intrinsically produces slow positronium, and efficiently too.

In most of our experiments, Ps is produced from a mesoporous silica target grown on a silicon substrate. Ps, initially with energy of 1 eV, is emitted from the same side as the positrons enter the converter (“reflection geometry” production) and one can generally obtain Ps with final energy of approximately 50 meV.  Once produced inside granulated powders, such as silica or magnesium oxide (MgO), Ps will lose some of its energy by making collisions with the surrounding internal surfaces before being emitted into vacuum. Generally, more collisions means greater amounts of energy loss, therefore colder Ps. A silica target was fabricated so that the Ps traverses the whole thickness of the target to be emitted out of the opposite side after making the maximum amount of collisions with the internal surfaces (transmission geometry).  However, the internal spacing of this target was too large to efficiently cool Ps below 200 meV (~200 km/s), which is still hotter than Ps emitted from mesoporous silica. Ps can also be produced from MgO, albeit with a slightly higher initial energy of around 4 eV. Previous studies have indicated that this 4 eV energy is reduced down to energies of around 300 meV in a 6 μm thick MgO layer. So, that gave us an idea. If we make a thicker MgO layer to increase collisional cooling, Ps atoms could be produced with energies lower than 50 meV (Positronium emission from MgO smoke nanocrystals).

MgOblog
A scanning electron microscope (SEM) image of smoked MgO.

To make the MgO target, we set fire to a strip of magnesium ribbon and collected the smoke on a suitable substrate (tinted goggles and a fume cupboard are necessary as you might imagine). This procedure produces perfect cubic crystals, in a 30 μm MgO layer, that have a wide size distribution, as evident from the SEM image above. The substrate of our choice was a 50 nm silicon nitride film, as it allows us to implant the positrons into the SiN side, to make positronium in the SiN-MgO boundary, which is then emitted into vacuum from the opposite side in transmission geometry. In this configuration, Ps atoms will travel through the 30 μm thick MgO, making the maximum amount of collisions. For comparison, we can rotate the target by 180° so the positron hits the MgO side (“reflection geometry”) and Ps makes the least amount of collisions, for positrons which are implanted to a relatively shallow depth of only 100 nm. We expect colder Ps to be produced in the former case compared to the latter, due to the distance travelled by the Ps (30 μm vs 100 nm). These two orientations are shown below, including the positron pulse and the excitation lasers. VT and VG refer to voltages applied to the target and grid electrode to control the positron energy and electric field.

MgOblog2
Experimental setup showing the target utilised in reflection and transmission geometry.

Once positronium atoms are emitted in either of the two set-ups, they are excited with UV and IR lasers to measure the Doppler profile, which gives an indication of their kinetic energy, KE. In the “reflection geometry” configuration, VT controls how deep into the MgO layer the positrons are implanted. Higher voltages results in deeper implantation, hence larger amount of collisions made by the Ps on their way out and colder Ps. However in the “transmission” set-up, around 2 keV voltage on VT is enough to make the positrons go through the SiN and form Ps in MgO. We found that for the 2 – 5 keV range we measured, positron penetration depths into the MgO layer in transmission set-up were essentially the same, meaning that Ps always travelled through 30 μm of MgO in this configuration. The resultant KE obtained from the Doppler profiles are shown below.

KEfit2
Left: An example of a Doppler profile. Right: Kinetic energies obtained from the Doppler profiles.

Surprisingly, Ps appears to be emitted with the same energy regardless of the amount of collisions it makes with the smoked MgO surfaces. This is inconsistent with the idea that Ps is formed in MgO with 4 eV of energy and reduction in energy takes place due to the collisions. If this is true then we expect KE in reflection set-up, when VT is 1 kV, to be very close to 4 eV. However, Ps kinetic energy is always around 400 meV. This is because Ps, in smoked MgO, is intrinsically produced with around 300 meV of energy with a wide distribution due to the grain sizes, and because of the large open volumes between the MgO crystals, cooling is rather inefficient.

This rules out smoked MgO as a candidate for cold Ps production but there are many experiments where the Ps production and interaction region needs to be separated from the positron beam line. In such experiments, a simple and easily producible MgO target as discussed here, in “transmission geometry” configuration, can be employed where, for example, a scattering gas cell can be installed without interfering with the incoming positrons.

We have also noticed some interesting observations when the lasers are fired into the MgO rather than travelling just in front of the MgO surface. More on that in the next blog post.

Towards enhanced interferometry using quantum states of light

On Wednesday 17th of October we had the pleasure to welcome Dr. Chris Wade from Oxford University to give a seminar to the AMOPP group about progress towards interferometry with exotic quantum states of light, more specifically Holland-Burnett states. This was a very interesting talk with a great mix of theory and experimental results. The abstract can be seen below.

Towards enhanced interferometry using quantum states of light

Quantum metrology is concerned with the enhanced measurement precision that may be gained by exploiting quantum mechanical correlations. In the scenario presented by optical inteferometry, several successful implementations have already been demonstrated including gravitational wave detectors [1], and lab-scale experiments [2,3]. However there are still open problems to be solved, including loss tolerance and scalability. In this seminar I will present progress implementing loss-tolerant Holland-Burnett states [4], and work searching for other practical states to implement [5].

[1] Schnabel et al. Nat. Comm. 1. 121 (2010)
[2] Slussarenko et al. Nat. Phot. 11, 700 (2017)
[3] Yonezawa et al. Science, 337, 1514 (2012)
[4] Holland and Burnett, PRL, 71, 1355 (1993)
[5] Knott et al, PRA, 93, 033859 (2016)

The Measurement Postulates of Quantum Mechanics are Redundant

On Wednesday 10th October we had Dr. Luis  Masanes from within the UCL AMOPP group give a very interesting seminar. His talk was focused on the fundamental questions posed by the measurement postulates of quantum mechanics, and how they are redundant given the other postulates that form the basis of quantum mechanics. Dr. Masanes was kind enough to provide a copy of his slides here and the abstract can be seen below.

The Measurement Postulates of Quantum Mechanics are Redundant

Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. The theorem presented in this work shows that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born’s rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as “unitary quantum mechanics”. This result unveils a deep connection between the dynamical and probabilistic parts of quantum mechanics, and it brings us one step closer to understand what is this theory telling us about the inner workings of Nature.

State-selective field ionization of Rydberg positronium

All atomic systems, including positronium (Ps) can be excited to states with high principal quantum number n using lasers, these are called Rydberg states. Atoms in such states exhibit interesting features that can be exploited in a variety of ways. For example, Rydberg states have very long radiative lifetimes (on the order of 10 µfor our experiments). This is a particularly useful feature in Ps because when it is excited to large-n states, the overlap between the electron and positron wavefunction is suppressed. Therefore the self-annihilation lifetime becomes so large in comparison to the fluorescence lifetime, that the effective lifetime of Ps in a Rydberg state becomes the radiative lifetime of the Rydberg state. Most Rydberg Ps atom will decay back to the ground state first, before self-annihilating [Phys. Rev. A 93, 062513 (2016)]. The large distance between the positron and electron centers of charge in certain Rydberg states also means that they exhibit large static electric dipole moments, and thus their motion can be manipulated by applying forces with inhomogeneous electric fields [Phys. Rev. Lett. 117, 073202 (2016), Phys. Rev. A 95, 053409 (2017)]

In addition to these properties, Rydberg atoms have high tunnel ionization rates at relatively low electric fields. This property forms the basis for state-selective detection by electric field ionization. In a recent series of experiments, we have demonstrated state-selective field ionization of positronium atoms in Rydberg states (n = 18- 25) in both static and time-varying (pulsed) electric fields.

The set-up for this experiment is shown below where the target (T) holds a SiO2 film that produces Ps when positrons are implanted onto it. The first grid (G1) allows us to control the electric field in the laser excitation region, and a second Grid (G2) with a varying voltage provides a well defined ionization region. An electric field is applied by either applying a constant voltage to Grid 2 as in the case of the static field configuration, or by ramping a potential on Grid 2 as in the case of the pulsed field configuration.

Figure 1: Experimental arrangement showing separated laser excitation and field ionization regions.

In this experiment we detect the annihilation gamma rays from:

  • the direct annihilation of positronium

  • annihilations that occur when positronium crashes into the grids and chamber walls

  • annihilations that occur after the positron, released via the tunnel ionization process, crashes into the grids or chamber walls

We subtract the time-dependent gamma ray signal when ground state Ps traverses the apparatus from the signal detected from Rydberg atoms when an electric field is applied in the ionizing region. This forms a background subtracted signal that tells us where in time there is an excess or lack of annihilation radiation occurring when compared to background (this SSPALS method is described further in NIM. A  828, 163 (2016)  and and here).

 

Static Electric Field Configuration

In this version of the experiment, we let the excited positronium atoms fly into the ionization region where they experience a constant electric field. In the case where a small electric field (~ 0 kV/cm) is applied in the ionizing region, the excited atoms fly unimpeded through the chamber as shown in the animation below. Consequently, the background subtracted spectrum is identical to what we expect for a typical Rydberg signal (see the Figure below for n=20). There is a lack of ionization events early on (between 0 and 160 ns) compared to the background (ground state) signal that manifests itself as a sharp negative peak. This is because the lifetime of Rydberg Ps is orders of magnitude larger than the ground state lifetime.

Later on at ~ 200 ns, we observe a bump that arises from an excess of Rydberg atoms crashing into Grid 2. Finally, we see a long positive tail due to long-lived Rydberg atoms crashing into the chamber walls.

 

Figure 2: Trajectory simulation of Rydberg Ps atoms travelling through the ~0 V/cm electric field region (left panel) and measured background-subtracted gamma-ray flux , the shaded region indicates the average time during which Ps atoms  travel from he Target to Grid 2 (right panel).

On the other hand, when the applied electric field is large enough, all atoms are quickly ionized as they enter the ionizing region. Correspondingly, the ionization signal in this case is large and positive early on (again between 0 and 160 ns). Furthermore, instead of a long positive tail, we now have a long negative tail due to the lack of annihilations later in the experiment (since most, if not all, atoms have already been ionized). Importantly, since in this case field ionization occurs almost instantaneously as the atoms enter the ionization region, the shape of the initial ionization peak is a function of the velocity distribution of the atoms in the direction of propagation of the beam.

 

 

Figure 3: Trajectory simulation of Rydberg Ps atoms travelling through the ~2.6 kV/cm electric field region (left panel) and measured background-subtracted gamma-ray flux , the shaded region indicates the average time during which Ps atoms  travel from he Target to Grid 2 (right panel).

We measure these annihilation signal profiles over a range of fields and calculate the signal parameter S. A positive value of S implies that there is an excess of ionization occurring within the ionization region; whereas, a negative S means that there is a lack of ionization within the region with respect to background. Therefore, if S is approximately  equal to 0%, only half of the Ps atoms re being ionized. A plot of the experimental S parameter for different applied fields and for different n’s is shown in the plot below.Figure 4: Electric field scans for a range of n states ranging from 18 to 25 showing that at low electric fields none of the states ionize (thus the negative values of S) and as the electric field is increased, different n states can be observed to have varying ionizing electric field thresholds.

It is clear that different n-states can be distinguished using these characteristic S curves. However, the main drawback in this method is that both the background subtracted profiles and the S curves are convoluted with the velocity profile of the beam of Rydberg Ps atoms. This drawback can be eliminated by performing pulsed field ionization.

Pulsed Electric Field Configuration

We have also demonstrated the possibility of distinguishing different Rydberg states of positronium by ionization in a ramped electric field. The set-up is the same as in the static field scenario but now instead of fixing a potential on Grid 2, the potential on this grid is decreased from 3 kV to 0 kV hence increasing the field from 0 kV/cm to ~ 1800 kV/cm (the initial 3kV is necessary to help cool down Ps [New J. Phys17,043059 (2015)]).

The advantage of performing state selective field ionization this way is that we can allow most of the atoms to enter the ionization region before pulsing the field. This eliminates the dependence of the signal on the velocity distribution of the atoms and thus the signal is only dependent on the ionization rates of that Rydberg state in the increasing electric field.

Below is a plot of our results with a comparison to simulations (dashed lines). We see broad agreement between simulation and experiment and, we are able to distinguish between different Rydberg states depending on where in time the ionization peak occurs. This means that we should be able to detect a change in an initially prepared Rydberg population due to some process such as microwave induced transitions.

Figure 5: Pulsed-field ionization signal as a function of electric field for a range of n states.

The development of state selective ionization techniques for Rydberg Ps opens the door to measuring the effect of blackbody transitions on an initially prepared Rydberg population and a methodology for detecting transitions between nearby Rydberg-levels in Ps. Which could also be used for electric field cancellation methods to generate circular Rydberg states of Ps.