How do single photons "play" with single atoms? | A Brief History of Quantum

"Trapping" atoms

The idea that atoms can be trapped by single photons in a cavity was proposed as early as 1991 by Serge Haroche and colleagues at the Ecole Normale Supérieure in Paris, and Berthold-Georg Englert, then at the Max Planck Institute for Quantum Optics in Garching, and colleagues also independently proposed the idea.

Both groups suggested dropping the atom into a microwave cavity where it might be trapped by a field generated by a single photon. Capture occurs when the potential energy depth is greater than the kinetic energy of the atom. The potential energy depth is related to the square root of the energy density of the photons in the cavity. However, the energy of microwave photons is small, while the cavity volume, determined by wavelength, is large. Obviously, traps made with microwaves are too shallow to capture atoms passing through the cavity under gravity.

The key to making smaller, deeper traps is to replace microwaves with optical photons of shorter wavelengths. For example, high-intensity visible light is now routinely used to manipulate the motion of colloidal particles, living cells and atoms. These "optical tweezers" can hold objects in the focal region of a laser beam.

In addition, lasers have been used to slow down or "cool" atoms: a method that has been widely used in both basic and applied research. For example, exotic quantum states known as Bose-Einstein condensates, high-precision atomic clocks, and ultrasensitive rotational and gravitational sensors all employ cold atoms.

Laser-cooled trapped ions are also prime candidates for optical-frequency standard or scalable quantum computers, which could, in principle, outperform conventional computers in certain tasks.

However, all of these experiments use a large number of photons to manipulate the motion of the atoms, since the field strength of a single photon is generally insufficient to trap the atom. And none of the experiments are sensitive enough to track the motion of individual atoms in real time.

However, this has recently changed thanks to the combination of laser cooling and trapping techniques with cavity quantum electrodynamics (QED) methods. Over the past decade, research on manipulating the optical properties of atoms using cavities made of high-quality mirrors has come a long way.

The light field inside a tiny optical cavity with highly reflective walls can now trap a slow-moving atom.

Earlier in 2000, Jeff Kimble of the California Institute of Technology (Caltech) and collaborators from Caltech, the University of Auckland in New Zealand, and a team of researchers at the author's Max-Planck-Institute for Quantum Optics (MPQ) in Garching, Germany, independently reported that this unique combination of techniques makes it possible to capture and track a individual moving atoms possible.

Both research groups used highly reflective mirrors to form a highly detailed optical cavity, and the number of round trips the light completed through the cavity nearly broke records. In these experiments, the cavity contained only one photon on average, thus acting as a single-photon optical tweezer.

Detection of individual atoms

When the energy of a light beam matches the energy difference between two electron levels in an atom (i.e., when the light is in resonance with an atomic jump), a large sample of atoms can be detected by light.

The atoms absorb the light, thereby reducing the photon flux transmitted through the sample. This effect is large enough to be easily measured when the sample contains at least a few thousand atoms. However, the detection of only individual atoms is never easy. In particular, the attenuation of the beam due to the presence of individual atoms is too small to be detected in the fluctuations or "noise" of the laser intensity.

In fluorescence imaging, where individual ions or atoms absorb and emit photons while stationary in the trap, the noise problem is less severe. Although this imaging technique has become routine, it must be noted that the available signal is severely limited by the photon scattering rate and the solid angle of the detection system. Long integration times are usually required to observe the particles, making this detection scheme unsuitable for tracking the motion of individual atoms with high spatial and temporal resolution.

However, non-resonant light can overcome the drawbacks of resonant detection schemes. In this case, instead of absorbing or emitting light, individual atoms change the phase of the incoming light wave - an effect that can be attributed to the refractive index of the atom.

Of course, the refractive indices of individual atoms are small, but in a high-finesse cavity, the effect is enhanced by the fact that the light travels back and forth between the cavity mirrors many times. For example, a cavity with a high finesse of 500,000 means that the mirrors reflect light about 160,000 times. In this way, the circulating light probes the atoms again and again, resulting in a large phase shift after many round trips.

It follows that the refractive index of even a single atom in the cavity can significantly change the length of the optical path between the mirrors. As a result, the atoms are able to tune the cavity to the resonant frequency or resonant frequencies of the light emitted from the external laser. (The resonant frequency or wavelength of the cavity is determined by the spacing of the mirrors). With the laser frequency fixed, moving atoms cause the intensity of light transmitted through the cavity to change: this effect can be easily measured when the cavity resonance is narrow.

The resonant light can also be used to observe the atoms in the cavity. In this case, the refractive index does not change, but the absorption of light is large. This absorption decreases the transmittance of light in the cavity and increases the reflectance - it is surprising that a single atom in the cavity can have such a large effect.

This effect was first observed by Hideo Mabuchi and his collaborators at Caltech in 1996, when a single atom was slowly traveling through a high-finesse cavity.

cavity quantum electrodynamics

But what is the optimum intensity of light needed to detect individual atoms? Intuitively, one would think that the signal-to-noise ratio would increase as the intensity of the illuminating laser increases, making a strong laser beam more useful than a weak one.

However, a strong laser beam can easily excite an atom to a high-energy state, depriving it of the ability to absorb more light - an effect known as saturation. At this stage, the atomic medium becomes transparent.

Saturation also changes the refractive index of the atoms. For sufficiently intense lasers, this refractive index approaches that of a vacuum. In this case, the atoms can no longer move the phase of the light wave. When the intensity exceeds a certain value, saturation makes it difficult for individual atoms to be detected by absorption or changes in the refractive index of the cavity.

But just how large is this upper intensity limit?

For the cesium and rubidium atoms in the Caltech and MPQ experiments, saturation occurs at moderate intensities. Since intensity is proportional to the number of photons per cavity volume, the number of photons needed to saturate the atoms decreases as the cavity size gets smaller. In recent experiments, the spacing between mirrors was as small as 10 microns. In such tiny cavities, atoms saturate even when less than one photon is present on average, which explains why the power level used in these experiments was about 1 picowatt (10^-12 watts)-equivalent to about one cavity photon.

The saturation problem is particularly acute when the light resonates with the atomic jump frequency. For non-resonant light, more photons are needed to saturate the atoms, thus relaxing the limit on light intensity.

What happens when the light intensity is sufficient to saturate an atom? In this case, the atom spends a significant portion of its time in an excited state. It can be returned to the ground state by spontaneous radiation or by stimulation of the light field in the cavity (which is a much faster process). When the intensity of the light field is greater, the atom is more likely to emit photons by stimulated emission.

In a small cavity, a single photon field is strong enough to stimulate the decay of the excited atomic state. Surprisingly, the photon does not need to be in the cavity before it begins to emit. Spontaneous emission causes a photon to enter the cavity, which excites its own emission. Thus, the excited atom radiates energy into the cavity rather than into the free-space continuum outside the cavity.

If the nuance is large, the photon is stored in the cavity and periodically absorbed by the atom, then re-emitted into the cavity several times before finally disappearing into the environment outside the cavity. This novel oscillatory radiation property is typical of the so-called cavity QED strong coupling mechanism, in which the coherent coupling of individual atoms to individual photons makes spontaneous radiation a reversible process.

These radiation properties have been studied by many research groups around the world, but the motion of atoms under these conditions can now only be explored by a new generation of cavity QED experiments.

The force of light

Radiation pressure is probably the best known of the forces exerted by light on atoms. In this case, the atom absorbs the resonant light and is hit by a momentum shock in the direction of the laser beam.

Although the atom's momentum changes again when it spontaneously emits a photon, the direction of this second momentum is completely random and thus averages to zero after several absorption-emission cycles.

On the other hand, induced leaps generate the so-called dipole force. The classical understanding of this force is that the electric field driving the laser induces mechanical oscillations of the atomic electrons. The resulting oscillating dipole moment is subjected to a force in an optical field with an intensity gradient (e.g., standing wave).

The magnitude of this force depends on the "detuning" of the laser with respect to the atomic transition frequency. For example, when the laser frequency is lower than the atomic frequency, the induced atomic dipole oscillates in phase with the driving laser field, and the atoms are attracted to the region of high intensity in the same way that a small piece of paper is attracted to a charged object.

Thus, the dipole force traps particles in the focal region of the "red-tuned" laser beam. For "blue-tuned" lasers (i.e., where the laser frequency is higher than the transition frequency of the atoms), the phase of the dipole oscillations with respect to the laser is deviated, so that the atoms are repelled from the high-intensity region.

Inside the cavity, the radiative properties of the atoms change, which has a dramatic effect on the force that light can produce. Since moving the atoms causes the field intensity within the cavity to change with position, new effects can arise. For example, in 1997, Peter Horak of the University of Innsbruck, Austria, and his collaborators suggested that atoms may be cooled as they move through the nodes and antinodes (i.e., minima and maxima) of a standing wave cavity.

To explain this cooling mechanism and to illustrate why the cavity plays a crucial role, let us consider a situation in which the strong coupling of atoms at the antinode enhances the intensity of the light field in the cavity, in which case the laser light is red-tuned with respect to the atoms so that the dipole force attracts the atoms toward the antinode. As a result, the moving atom decelerates as it approaches a neighboring node. When the atom reaches that node, its coupling to the cavity mode disappears and the intensity of the light field decreases.

As a result, the atom will move in the dark as it approaches the next antinode, gaining very little kinetic energy, certainly not enough to make up for the previous loss.

Because of this, too, the motion of the atoms is slowed down, simply because the field inside the high-mass cavity cannot be adjusted quickly enough to the motion of the atoms. Unlike conventional laser cooling where atoms are slowed down by spontaneously emitting photons, the dissipation mechanism in cavity cooling involves the loss of photons in the cavity. Using this cavity-mediated "friction", it is possible to cool molecules that cannot be cooled by standard laser cooling techniques.

Cavity-mediated cooling is interesting because it can complement other recently developed techniques for trapping molecules.

However, in addition to changing the strength of the field inside the cavity, atoms that periodically exchange energy with the cavity cause rapid fluctuations in the amplitude and phase of the optical field.

Since the trapping potential is determined by the optical field inside the cavity, these changes lead to fluctuations in the optical force. In turn, these fluctuations affect the momentum of the atom in a stochastic manner, usually by increasing the velocity of the cold atom to heat it.

atomic cavity molecule

A remarkable feature of the cavity-QED scheme is that even if there is only one photon in the cavity, the trap is deep enough to hold a laser-cooled atom. Since the electric field per photon is large, the optical force per photon is also large, making it possible to trap a single photon in a small cavity.

But to trap atoms in a photon dipole potential requires one more trick: the potential cannot be turned on until the approaching atom reaches the center of the cavity. Otherwise, an atom that falls into the trap from one side will escape from the other, just as a marble that rolls into a bowl will roll out again without being captured.

Since we can now observe the position of the atoms in a cavity field that contains, on average, less than one photon, we can turn on the potential at the right moment.

The atom's entry into the cavity causes an increase in light transmission from the external laser, which triggers the switch and increases the power driving the laser. If timed correctly, the atom is captured at the antinode of the standing wave dipole potential for up to a few milliseconds - which is about ten times longer than it would have stayed in the cavity if it had not switched.

The large oscillations evident in the transmission intensity reflect the motion of the captured atom. In particular, the transmittance is large when the atom is in the center of the cavity and decreases as the atom moves away from the cavity axis.

At first glance, capturing an atom with a single photon in a cavity appears to be similar to capturing an atom with a laser beam in free space; the difference is that the intensity enhancement in the cavity allows us to use a weak laser. However, the strong coupling of atoms to a cavity requires a conceptually different description, which we can understand by borrowing a simple picture from chemistry.

Just as two protons in a hydrogen molecule can be surrounded by symmetric (i.e., bound) or antisymmetric (antibound) electronic wavefunctions, atomic dipole moments can oscillate either in phase (bound) or out of phase (antibound) with the light field in an atom-cavity system.

Both states of the atom-cavity "molecule" contain a quantum of energy that can oscillate between the atom and the cavity. This quantum is therefore shared between the atom (as an electron excitation) and the cavity (as a photon), just as the electron in a hydrogen molecule is shared by two protons.

This sharing means that atomic capture also leads to photon capture. In this case, the presence of an atom with a long-lived excited state extends the residence time of the photon in the cavity.

Reconstructing atomic trajectories