Direct Observations and Measurements of Single Atoms

One of the fundamental principles of quantum mechanics tells us that the energy of an ion (or atom) is quantized. The specific energy levels at which the atom is (relatively) stable correspond to different shells and orbitals, as may be familiar to students from descriptions of the Bohr atom. In this experiment, we use barium ions, whose lowest energy levels can be drawn as shown in Fig. 1. Key here is that these levels are distinct and that the differences in energy between any pair is unlike the others. There are many more levels, but these are the most relevant. When an ion in the ground state (6 S_1/2) absorbs energy in the form of light, if the light supplies exactly the right amount of energy, it may bring the ion to the excited state (6 P_1/2). This primary transition for barium occurs at an energy corresponding to 493-nm laser light. The ion remains in the excited state for a short time (7.9 ns) before decaying back to the ground state due to either spontaneous or stimulated decay. From there, it is excited again by the laser and decays rapidly once more. Under continuous excitation by the laser, this transition scatters photons at a rate on the order of one million decays per second per ion. If we collect some of these using a lens and focus them, we can see the photons from the atom as coming from a point—these photons are bright green and allow the atoms to be seen by eye in our exhibit.

However, if we excite the barium ion with 455-nm light, it goes into the 6 P_3/2 state. From there, it sometimes decays to another state (5 D_5/2), as shown in Fig. 1. This state is very long lived—when the ion arrives there, it will stay there for an average of 31 s (about 4 billion times longer than for the 6 P_1/2 state!)—which is why we call it a “metastable” state. If the ion gets into this metastable state, the 493-nm laser is no longer able to excite the ion. Therefore, for a long time, we see no photons; hence, we refer to this as the dark state. When the dark state does decay, the ion returns to the bright (6 S_1/2) state, where it suddenly starts scattering photons. This sudden switching between the bright and dark states is called a quantum jump and was first observed for barium ions in the 1980s.⁴ 

In our experiment, we use a linear quadrupole trap⁵ to confine the barium ions [see Fig. 2(a)]. Note that excellent demonstrations of quadrupole trapping of charged spores already exist for the classroom.^6,7 However, in our case, the charges are singly charged atoms, so 50,000 times smaller than the spores! Our trap is 4 cm in length and consists of a quadrupole arrangement of blade-shaped electrodes that are parallel to a central line, with two cylindrical end-cap electrodes arranged on the center line at either end. By applying alternating voltage at megahertz frequencies, the resulting oscillating quadrupole fields confine the ions radially, while static voltages applied to the end caps confine them along the central line. Thus, the ions become arranged in a linear chain with a spacing on the order of 10 µm due to the repulsion between the individual positively charged ions.

We use two lenses with a large collection angle, placed symmetrically around the trap, to collect approximately 24% of the light emitted by the ions. The entire setup is then enclosed in a cylindrical vacuum chamber with an objective on one side of the chamber and camera on the opposite side as shown in Fig. 2(b). This geometry makes it possible to see the ions not only by eye (with a factor of 200 magnification), but also on a camera (with a factor of 10.6 magnification). The view from the camera is shown in Fig. 2(c).

Each visible spot contains the light coming from a single ion, but key to differentiating the single ions is the large spacing between them. The size of each spot is mainly limited by the optical diffraction limit of the setup optics and eye, though when the ions heat up or wobble in the oscillating fields, the image may blur slightly. The elongation of the spots in Fig. 2(c) is due to an asymmetry in the trap.

In the initial state of the experiment, the 493-nm laser is on, and one can observe a row of glowing points—the ions. By pushing a button, a blue LED located on the left side of the vacuum chamber is turned on. A small number of ions (typically 1–2) will absorb the resulting 455-nm light and then decay into the long-lived dark state. After some time, the ions will decay back to the ground state, at which point they will suddenly become bright again—a clear visualization of quantum jumps.

To convince themselves that every glowing point represents a single ion already poses a demanding and inspiring task for students. To aid the process, they can continue to explore the quantum properties of the ions by interacting with the experiment. First, they can observe that certain transitions can only be excited by particular wavelengths of light. The 493-nm light, which is always on, is only sufficient to excite the bright transition. To excite the ion into the dark state, a different color of light is required, which comes from the blue LED. The two levels of light emission are also direct evidence of the different quantized energy states of the ions. Second, the fact that only individual ions go dark, causing gaps to form in the ion chain, is evidence that these points of light are indeed single ions, and that the ion is still there (there is still a charge there keeping the other atoms in place) but simply not visible. Thus, as a first qualitative functionality, the experiment offers the possibility of building conceptual understanding of basic quantum properties of single atoms.

There exists a second, quantitative functionality of the ion trap. Using observations of the dark state, students are in fact able to measure the lifetime (31 s) of the dark state.⁸ As each ion is identical in nature and each has the same probability of decay at any point in time, the dark state decay times follow an exponential distribution.⁹ While a single measurement yields no information about the timescale due to the nondeterministic nature of the quantum jumps, by measuring the decay events over many trials, one can extract the excited state lifetime from the resulting distribution.

The experiment therefore allows students to collect their own data on the lifetime of a quantum state. To support students’ understanding of the process, one can draw a connection to measuring the half-life of a radioactive sample, a process students may be familiar with. However, while in the measurement of a radioactive sample, the students experience the average effect of around 10²³ atoms giving exponential decay, here they see that they can build this from single events! Students can also perform a data analysis by formulating their data into a histogram and fitting the resulting (discrete) distribution using their favorite programming language, linearizing the exponential and extracting the lifetime from the slope, or reading off the lifetime directly.

This experience therefore may be adapted to the prior knowledge of students by offering more qualitative options to introduce basic quantum principles but also quantitative measurements, which require more advanced understanding and experimental skills.

We tested the latter experiment with two groups of upper secondary students around the age of 16 as well as one group of science teachers. Over the course of an hour, a subset of each group performed the experiment described above—the promotion of single ions to the dark state and the measurement of time spent in this state. This measurement is performed using a stopwatch or smartphone. Since multiple ions may become dark at once, it is also possible to perform several measurements per button push by using the lap function on the stopwatch. The timer is started at the point in time where the ions go dark and stopped (or lapped) as soon as one observes the ion become bright again. Due to the reaction time of participants, and the fact that not all ions go dark simultaneously, the error on a measurement is typically on the order of a second.

During the 1-hour measurement period, the participants were able to collect around 30–40 data points. Several sets of results are summarized in Fig. 3. The group was then asked to explain the experiment and their results to the other participants who had not taken part. They were mostly able to correctly explain the main concepts—that the ion trap confines the ions, that they are excited by a laser and may be temporarily excited into a dark state using a blue light, and that by measuring the time in the dark state, one is able to determine the lifetime of the state. However, we also observed difficulties in student explanations. A prominent example that has already been reported in several studies at the college level^10,11 was that students confused electric fields in the ion traps with magnetic fields.

The experiment presented in this article allows students of varied ages and backgrounds to experience material typically only discussed in theory¹²: observing single ions and their energy levels and quantum jumps. Furthermore, the optional quantitative measurement allows them to deepen these concepts. The experiment can also be used as a basis to discuss further interesting applications of quantum mechanics, such as atomic clocks, quantum cryptography, and quantum computers. In the latter, a bright ion can be thought of as having the logical state 0, while dark corresponds to 1.

Clearly the setup is not one that can be readily copied for deployment in a school. To open this experience to many students, the ion trap is currently located in the Swiss Science Center Technorama. The Technorama is the largest nonformal place of learning in Switzerland and hosts nearly 300,000 visitors every year, making it an excellent place to house such an exhibit.¹³ We have created an interactive experience surrounding the ion trap, which allows all visitors to see and interact with the ions. Furthermore, classes from all over Switzerland and surrounding areas can book workshops, during which time, they are able to perform the experiment we have described here. An online platform prototype (see the “Access” section below) has been created to allow teachers and students to access the ion trap and its full functionality from the comfort of their classroom.

For access to the online version of this experiment, please contact didaktik@technorama.ch. A sample lab procedure can also be provided if desired. The duration of the experiment is approximately 1.5 hours and is suitable for students ages 15 and up, provided they have had an introduction to atoms and exponential decay.

The authors thank the members of the Swiss Science Center Technorama for their support and for helping to make this project possible.