Detecting and Imaging Magneto-Optically Trapped Rubidium-85 Ions Through Near-Field

Scanning Optical Microscopy

Dario O. Scotto

Department of Physics, Montana State University, Bozeman, MT

(12 December 2016)

Abstract

An electro-optical design for the experimental trapping and imaging of trapped rubidium-85 ions is given.

Techniques from Near-field Scanning Optical Microscopy are implemented in the probe and detection

aspects of the design. Etched fibers are chosen for their geometric properties so that a sample of trapped

ions on the order less than a single nanometer may be detected with little disturbance. These detection

techniques are paired with two trapping methods so that the rubidium-85 ions may be isolated and

imaged. Three orthogonally crossed beams tuned to just below the rubidium-85 D2 transition line will be

employed to produce an optical molasses that will cool the rubidium-85. This trap will be assisted by a

magneto-trap consisting of an anti-Helmholtz coil pair to take advantage Zeeman shifting for further

cooling and confinement. A crash course introduction into the theoretical concepts central to this

experiment is given such that the purpose of all elements of the design may be understood.

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Presented here is the outline of the employment of NSOM techniques to detect and manipulate trapped

rubidium ions. The design thus far is tentative and is part of the undergraduate research I am undertaking

with Dr. Alan Craig, a resident research professor at Montana State University. If our efforts with

rubidium are successful then the prospects of trapping electrons will be explored. Information researched

from a number of distinct fields will contribute to the overall process of design. These include techniques

and tools used in near-field scanning optical microscopy, electromagnetism, quantum optics, and control

theory.

Fig. 1.1

Near-field Scanning Optical Microscopy (NSOM), is a form of microscopy employed to achieve ultra-

high optical resolution of a sample to be characterized and studied. The defining technique of NSOM is

the use of a sub-micron optical probe positioned a distance from the object to be sampled. This distance is

sub-wavelength of the source used and is known as the near-field (Fig. 1.1). This region is particularly of

use because the evanescent waves associated with the light passed through the probe will not be limited

by their later diffraction. This breaking of the far-field limit allows for high spatial, spectral, and temporal

resolving power. Lateral resolutions of 20nm and vertical resolution of 2-5nm have been achieved, a very

small fraction of a wavelength as opposed to typical 200-300nm of conventional optical imaging

methodologies [1]. An advantage which NSOM has over diffraction-limited optical microscopy is that the

spatial resolution is not limited by the wavelength of the incident light or by the numerical aperture of any

other components. The use of this highly collimated evanescent near-field requires that the probe be in

constant feedback to maintain its subwavelength distance from the sample. To fall within the near field

distance and avoid coming into contact with the sample, which can lead to damage of both the probe and

sample, the probe must be precisely controlled with a with a feedback control system. A chosen set point

(voltage difference for eg.) is compared to a measured value, the error is then gauged and sent through a

Proportional-Integral-Derivative (PID) controller which corrects for this error such that the error is

minimized over time (this is another focus which we have been pursuing, but for the purposes of the

design it is not necessary to discuss). The monitoring of the probe through feedback additionally confers

the experimenter with the ability to also “chase” a sample, particularly if the sample is something very

small, like a super cooled atom.

Due to its effectiveness and do-it-yourself customizability a popular probe choice, and one which we will

use, is an optical fiber. The ability to perform NSOM demands that specific physical requirements be met

when selecting candidates for probes. The probe geometry must be such that its terminal has a well-

defined sub-wavelength aperture and can easily access the sample. These needs are readily met by tapered

optical fibers. A tapered fiber can be achieved through two methods, pulling and etching. Pulling the fiber

involves applying gradient heat along the fiber’s length while a tensile force applied to stretch the fiber.

This method will sometimes simultaneously taper the cladding and core evenly. Occasionally when the

fiber is cleaved fracturing occurs which may influence the light coupling. It may be desirable to avoid this

and look to other tapering methods, although the coupling does not seem to be significantly affected in

one study [2].

Fig. 1.2

Etching a fiber can be used to achieve the desired taper as an alternative to heat-pulling. In this method it

is custom to remove part of the fiber cladding to expose the core, followed by partial removal of the core,

such that a gradual transition into the core is achieved. An ammonium fluoride buffered hydrofluoric acid

solution is commonly used as an acid bath to immerse the fiber end (Fig. 1.2). The solution has a

calculable etch rate such that one can get very precisely tapered ends. On different timescales one can

This method is quick, easily reproducible, and inexpensive. For these reasons, this method is the one we

will utilize throughout the NSOM techniques we have worked into our design. Cone angles between 36󠅣-

110◦ are achievable using this method and allow customizability for the probe to access the sample with

little disturbance if one chooses [3]. This trait conferred by the small cone angle would be desirable of a

probe if the sample were variable in its topography allowing for a highly accurate sample image, although

it offers poor light collection efficiency. Arguably the stretching method also suffers from these small

cone angles.

Our victim to be sampled through NSOM and other imaging techniques will be trapped ions and so we

needed a trap design. Our trap will involve electromagnetic, atomic, and Doppler effects to cool stable

rubidium-85 ions. Rubidium is an easily ionized metal, 24 such isotopes are known to exist, lending to its

prominent use in most applications requiring an ion source. Traps, photo cell manufacture, and ion

engines are but a short list of its applicability. As an alkaline metal, rubidium is one of the most

electropositive and it possesses electronic dipole transitions found in the infrared spectrum. Rubidium at

room temperature is also found to possess a vapor pressure of 10-7 Torr [4]. As a result, it is an excellent

candidate for research applications. Our design requires a great deal of involvement into ensuring that the

specifications of each component is able to handle the spectroscopic properties of these ions such that a

successful trap is designed.

Fig. 1.3a (Left), Fig. 1.3b (Right)

The fundamental principle of atomic cooling as a means for trapping involves the absorption and

emission of photons emitted by a source (Fig. 1.3a). As a photon comes zipping by an atom it may

become absorbed by the atom which then enters into a higher energy state. Yet quantum mechanics

ensures that due to the quantization of these energy states, the majority of these photons are actually

incapable of having any effect on the atom’s energy at all. Only photons possessing the frequency which

matches the difference in frequency between the atom’s present orbital and an excited orbital, will be

accepted, and promote the atom. Doppler cooling occurs if we tune the frequency of laser to just below

the frequency of the electronic transition line of the atom. For this reason, we will have an external cavity

diode laser tuned to the rubidium-85 D2 absorption line at 780.241368 nm (Fig. 1.3b) [5,6], such as a

MOGLabs ECD004 (Note that at this early in the stage of our design process our choice of laser is meant

to be tentative).

The atom can only accept the photons in this detuned beam if it moves in a direction antiparallel to the

beam. As a result, the atom will see incoming photons that were previously red shifted now blue shifted

as having the necessary resonance frequency due to the Doppler effect, and the atom will absorb it.

During each absorption the atom reach an excited state but receives a kick from the momentum carried by

the photon. The atom will spontaneously emit another photon as it relaxes to its ground state, which again

kicks the atom, this time in a random direction. The net motion due to these random kicks of the photon

will be zero in any direction not along the axis of the beam. Thus over many scattering cycles the atom

will experience a reduction of kinetic energy as it moves closer to the beam, resulting in the “cooling” of

the atom. The lower limit to the temperature of this cooling process for an atom is known as the Doppler

cooling limit, 𝐓 =ℏ𝛄

𝟐𝐤𝐁, where 𝛄 is the natural linewidth.

Fig. 1.4

To confine the ion in three dimensions we will employ a technique known as “optical molasses”. We will

cross three identical lasers (Fig. 1.4), all tuned to the same D2 line transition frequency of rubidium-85.

Ensuring that the lasers are orthogonal to one another we get an exact point in 3-space at which the ions

will be confined. Polarization gradient cooling offers an explanation for this phenomena. A standing wave

is formed by the counter propagating beams of circularly polarized light. The polarization of this wave is

linear but it rotates at a high rate along the direction of the beams and is spatially varied.

A further confinement assist for our trap will be taken in the form of a magneto trap. An anti-Helmholtz

coil pair. These are toroidal coils wrapped in opposing directions and are set up parallel to one another.

This results in a spatially varying magnetic quadrupole with zero field in the middle, to be concomitant

with the central position of the optical trap in our design. The addition of this field induces a Zeeman shift

in the magnetic sensitive mf levels of our ions, the strength of which increases with radial distance from

the center of trap. As a result, the atom will become more likely to receive a photon kick back towards the

center of the trap if it were to ever veer out of it.

A vacuum chamber will house our magneto-optical trap (MOT). The MOT cloud will only be able to

form in a vacuum chamber with a background pressure of less than 10 µPa. If this pressure were to be

exceeded our ions will be kicked out of the trap faster than they can be loaded into it.

We will seek a way to detect, and later image, these cooled ions as they are fluorescing. This is where

NSOM techniques will be naturally incorporated into our design. We have the option of utilizing optical

fibers either as probes for detection of as another style of trap-assist themselves (Fig. 1.4 – Left). When

an optical fiber is used as a trap it may be referred to as an optical tweezer. A Gaussian laser beam can be

delivered through an optical fiber with a molded lens-like tip. A strong electric field gradient exists at the

beam waist and a 2D optical trap results [7]. This could be an effective means to snatch ions and place

them in a location of the trap where we would like them, particularly useful if instead we devise a trap

with multiple wells, or perturb them if a crystalline-trap structure can be created.

If we decide to use our tapered fibers for fluorescence capture as a method of detection, there are

obstacles we must take into account. The solid angle of a fiber tip cannot be so small that it becomes

extremely unlikely for the entry of emitted photons. We must choose optical fibers with indices of

refraction of both the fiber cladding and core, such that we maximize the amount of light capture in the

cone. The numerical aperture of a fiber is NA = √ncore2 − nclad

2 will give us the range of angles over

which our fiber can accept or emit light. Assuming we overcome this, the next obstacle involves bringing

our fiber to a specific ion, which we will treat with NSOM techniques as our sample. It would be

necessary at this point to engineer an xyz-piezo mount for our fiber to ride on. Through the use of

aforementioned PID control, we wish to track the ion to optimize the intensity signal we detect. This

optical system will consist of our fiber leading to an APD to produce a current signal. If we were to pulse

our lasers with either a modulator or a chopper with a frequency set to the fluorescence of our ions, we

would have a pulsed signal. This signal will surely come with noise and once it is exits out of the APD it

will be passed into a Lock-In amplifier to pull our approximately 95% of the out-of-band noise, thus

improving our signal-to-noise ratio. From this will be able to image the trapped ions. Alternatively, we

may wish to instead employ a CCD array, in tomographic style, to image the trapped ions (Fig. 1.4 –

Right). This may prove to be a more effective way of imaging the ions as we will not have to deal with

difficulties in capturing emitted photons due to the fiber cone angles.

References

[1] Dürig, U.; et al. (1986). "Near-field optical scanning microscopy". J. Appl. Phys. 59 (10): 3318.)

[2] Sarangan, A. M. (2007). Tapering Optical Fibers. Retrieved December 09, 2016, from

https://udayton.edu/directory/engineering/electrooptics_grad/sarangan_andrew.php

[3] (Puygranier, B., & Dawson, P. (2000). Chemical etching of optical fibre tips — experiment and model.

Ultramicroscopy, 85(4), 235-248. doi:10.1016/s0304-3991(00)00069-3)

[4] Robinson, J., Liu, Y., & Shelton, D. (2014). Development and Characterization of a Magneto-Optical

Trap for Rubidium. Nevada State Undergraduate Research Journal, 1(1), 14-21.

doi:10.15629/6.7.8.7.5_1-1_f-2014_2

[5] Steck, D. A. (n.d.). Rubidium 85 D Line Data. Retrieved from

http://steck.us/alkalidata/rubidium85numbers.pdf

[6] Gardiner, S. (n.d.). Rubidium D2 Line. Retrieved December 09, 2016, from

http://massey.dur.ac.uk/gtp/RbD2line/RbD2line.html

[7] Single-beam optical fiber trap. (2007). Journal of Physics: Conference Series, 61, 1137-1141.

doi:10.1088/1742-6596/61/1/225

Appendix

MOGLabs External Cavity Diode Laser: Model ECD004

Wavelength/frequency

780 nm 60 mW standard. Up to 200 mW output power available.

369.5-1120 nm Contact MOGLabs.

Linewidth Typically 200kHz FWHM (self-heterodyne)

RF modulation 160 kHz – 2.5 GHz

Grating Standard: 1800 l/mm holographic Au

Tuning range Typically +/-5 nm for single diode 369 nm to 980 nm with different diodes.

MODEL SR830 DSP LOCK-IN AMPLIFIER