Today, almost 100 years after the birth of quantum mechanics, physicists are still learning about the interaction between light and matter.
At the beginning of the last century, one of the driving forces for the development of quantum mechanics was the need to understand why atoms can only emit light of a specific wavelength. Soon after, quantum mechanics was applied to molecules, and then to solids. On the other hand, quantum mechanics is also being applied to the properties of elementary particles, especially electrons.
Quantum mechanics has achieved great success in all of these areas. In fact, quantum electrodynamics, the theory of how light and matter interact, is the most powerful and precise theory of all physics. But what's even more amazing is that quantum theory still fascinates researchers.
One might think that 100 years after the advent of quantum mechanics, we will not know much about quantum mechanics. But that's not the case. Interest in quantum mechanics, both theoretical and experimental, is likely to be stronger now than ever.
So,How do physicists trap individual atoms in a small box or cavity that contains only one photon on average?That's what this article will be about
Atomic physicists can now capture individual atoms with a single photon and reconstruct their trajectories.
Atomic physicists are now able to observe the motion of individual atoms in real time with high spatial and temporal resolution, reconstruct their trajectories, and explore hitherto unknown "light forces". The realization of this "single-photon optical tweezers" opens up new possibilities for the control of internal and external quantum states of atoms, molecular cooling, and quantum information processing.
As early as 1991, Serge Haroche and his colleagues at the École Normale Supérieure in Paris proposed the idea that atoms could be trapped by a single photon in a cavity, and Berthold-Georg Englert, who was then working at the Max Planck Institute for Quantum Optics in Garching, and his colleagues 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. Trapping occurs when the depth of potential energy 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. But the energy of the microwave photon is small, while the volume of the cavity, which is determined by the wavelength, is large. Obviously, the trap made with microwaves is too shallow to capture atoms passing through the cavity under the action of gravity.
To create smaller and deeper traps,The key is to replace microwaves with optical photons with shorter wavelengths。For example, high-intensity visible light is now routinely used to manipulate the movement of colloidal particles, living cells, and atoms. These "optical tweezers" can clamp objects in the focal area of the laser beam.
In addition, lasers are used to slow down or "cool" atoms: this method has been widely used in basic and applied research. For example, strange quantum states known as Bose-Einstein condensates, high-precision atomic clocks, and ultra-sensitive rotation and gravity sensors all employ cold atoms. Laser-cooled trapped ions are also a prime candidate for optical frequency standards or scalable quantum computers, which, in principle, can outperform conventional computers in certain tasks.
However, all of these experiments use a large number of photons to manipulate atomic motion, as the field strength of a single photon is generally not strong enough to trap the atom. And none of the experiments is sensitive enough to track the movement of individual atoms in real time.
However, this has recently changed due to the combination of laser cooling and capture techniques with cavity quantum electrodynamics (QED) methods. Over the past decade, great progress has been made in manipulating the optical properties of atoms using cavities made of high-quality mirrors.
Now, the light field inside a tiny cavity with a highly reflective wall can trap a slow-moving atom.
Earlier in 2000, Jeff Kimble of the California Institute of Technology (Caltech) in the United States and collaborators from the California Institute of Technology, the University of Auckland in New Zealand, and the authors' research team at the Max Planck Institute for Quantum Optics (MPQ) in Garching, Germany, independently reported that this unique combination of technologies makes it possible to capture and track individual moving atoms in optical cavities.
Both research teams used highly reflective mirrors to form a high-definition optical cavity, and the number of round-trips in which light was completed in the cavity was almost a record-breaking. In these experiments, the cavity contains only one photon on average, thus acting as a single-photon optical tweezers.
When the energy of the beam matches the energy difference between the two electron levels in the atom (i.e., when the light resonates with the atomic transition), a large number of atomic samples can be detected with light.
Atoms absorb light, reducing the flux of photons transmitted through the sample. This effect is large and is easy to measure when the sample contains at least a few thousand atoms. But detecting only a single atom is no easy task. In particular, the attenuation of the beam due to the presence of a single atom is too small to be detected in fluctuations or "noise" in the intensity of the laser.
In fluorescence imaging, when a single ion or atom is at rest in a trap that absorbs and emits photons, noise is less of a problem. While this imaging technique has become routine, it must be noted that the available signal is severely limited by the photon scattering rate and the fixed angle of the detection system. It often takes a long integration time to observe particles, so this detection scheme is not suitable for tracking the motion of individual atoms with high spatial and temporal resolution.
However, non-resonant light can overcome the shortcomings of resonance detection schemes. In this case, the individual atoms do not absorb or emit light, but instead change the phase of the incoming light waves – an effect that can be attributed to the refractive index of the atoms.
Of course, the refractive index of a single atom is small, but in a high-finesse cavity, the effect is enhanced by the light going back and forth between the cavity mirrors many times. For example, cavities can be as fine as 500,000, which means that the specular surface reflects 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 can be seen that the refractive index of even one atom in a cavity can significantly change the length of the optical path between mirrors. As a result, the atom is able to adjust the resonance frequency or resonance frequency of the light emitted by the cavity with the external laser. (The resonant frequency or wavelength of the cavity is determined by the mirror spacing). In the case of a fixed laser frequency, the moving atoms cause a change in the intensity of the light transmitted through the cavity: this effect can be easily measured when the cavity resonance is narrow.
Resonant light can also be used to observe atoms in a cavity. In this case, the refractive index does not change, but the amount of light absorbed is significant. This absorption reduces the transmittance of light in the cavity and increases the reflectivity – a single atom in the cavity can have such a large effect, which is surprising.
This effect was first observed in 1996 by Hideo Mabuchi and collaborators at the California Institute of Technology, when a single atom was slowly passing through a highly detailed cavity.
Monoatomic detection. (a) Partial optical systems and vacuum systems for the capture of single atoms in high-definition optical cavities, at the Max Planck Institute for Quantum Optics in Garching, Germany. (b) In the MPQ experiment, rubidium atoms (green) collected and cooled in a magneto-optical trap are emitted upwards into a cavity 110 μm long and 430,000 fine. The light from a weak laser with a wavelength of 780 nanometers creates standing waves in the cavity, detecting atoms by measuring the light passing through the cavity. (c) If the wavelength of light resonates with an atom, then the presence of the atom is signaled by a decrease in transmittance. (d) The presence of atoms can be detected even if the light does not resonate with the cavity or atom by adjusting the external laser so that the cavity containing one atom resonates with the input light. In other words, atoms cause cavities to resonate with light, and each of the three peaks shown is characteristic of a single atom.
But what is the optimal light intensity required to probe a single atom?Intuitively, one would think that the signal-to-noise ratio increases with the intensity of the irradiated laser, so a strong laser beam is more useful than a weak laser beam.
However, a strong laser beam can easily excite atoms to a high-energy state, causing them to lose their 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 a laser of sufficient intensity, this refractive index is close to that of a vacuum. In this case, the atom 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 how big is this upper limit of intensity?
For the cesium and rubidium atoms in the Caltech and MPQ experiments, saturation occurs at moderate intensities. Since the intensity is directly proportional to the number of photons per cavity volume, as the cavity size decreases, the number of photons required to saturate the atom also decreases. In recent experiments, the spacing between mirrors was as small as 10 microns. In such tiny cavities, atoms reach saturation even if less than one photon is present on average, which explains why the power levels used in these experiments are about 1 picowatt (10 -12 watts) – equivalent to about one cavity photon.
The saturation problem is particularly acute when light resonates with atomic transition frequencies. For non-resonant light, more photons are required to saturate the atoms, relaxing the limit on light intensity.
What happens when the light is strong enough to saturate the atoms?In this case, the atom is in an excited state for a considerable part of the time. It can return to the ground state by spontaneous radiation or stimulation by a light field in a cavity, which is a faster process. When the intensity of the light field is high, atoms are more likely to emit photons by stimulated emission.
In a small cavity, the single-photon field is strong enough to stimulate the decay of the excited atomic state. Amazingly, the photons don't need to be in a cavity before they can start firing. Spontaneous emission causes a photon to enter the cavity, which excites its own emission. As a result, the stimulated atoms radiate energy into the cavity rather than into the free-space continuum outside the cavity.
If the nuances are large, the photons are stored in the cavity and periodically absorbed by atoms, then re-emitted into the cavity several times before disappearing into the environment outside the cavity. This novel oscillatory radiation characteristic is typical of the so-called cavity QED strong coupling mechanism, in which the coherent coupling of a single atom to a single photon makes spontaneous emission a reversible process.
These radiation properties have been studied by many research groups around the world, but the movement of atoms under these conditions can now only be explored through a new generation of cavity QED experiments.
Radiation pressure is probably the most well-known of the forces exerted by light on atoms. In this case, the atoms absorb the resonant light and are impacted by the momentum in the direction of the laser beam.
Although the momentum of the atom changes again when it spontaneously emits a photon, the direction of this second momentum is completely random and therefore averages to zero after multiple absorption-emission cycles.
On the other hand, inducing a jump generates what is known as a dipole force. The classical understanding of this force is that the electric field that drives the laser causes mechanical oscillations of atomic electrons. The resulting oscillating dipole moment is subjected to a force in a light field with an intensity gradient, such as a standing wave.
The magnitude of this force depends on the "detuning" of the laser relative to the transition frequency of the atom. For example, when the laser frequency is lower than the atomic frequency, the atomic dipole is induced to oscillate in phase with the driving laser field, and the atom is attracted to the region of high intensity, just as a small piece of paper is attracted to a charged object.
As a result, the dipole force can capture particles into the focal area of the "red-tuned" laser beam. For "blue-tuned" lasers (i.e., the laser frequency is higher than the atomic transition frequency), the oscillation phase of the dipole relative to the laser is skewed, so the atoms are excluded from the high-intensity region.
Within the cavity, the radiation properties of the atoms change, which can have a huge impact on the force that light can produce. Since moving atoms causes the strength of the field inside the cavity to change with position, a new effect is created. For example, in 1997, Peter Horak and his collaborators at the University of Innsbruck in Austria proposed that atoms could be cooled as they move through nodes and anti-nodes (i.e., minimum and maximum) through standing wave cavities.
To explain this cooling mechanism and illustrate why the cavity plays a crucial role, let's consider a case where the strong coupling of the atoms at the counter-node enhances the intensity of the light field in the cavity, in which case the laser is red-tuned relative to the atoms, causing the dipole force to attract the atoms towards the anti-node. As a result, the moving atoms slow down as they approach the neighboring nodes. When the atom reaches this node, its coupling with the cavity mode disappears and the light field intensity decreases.
As a result, the atom moves in the dark as it approaches the next anti-node, gaining very little kinetic energy, certainly not enough to compensate for the previous losses.
Because of this, the motion of atoms slows down, simply because the field in a high-quality cavity cannot be adjusted quickly to the motion of 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.
Single-photon tweezers. The entry of rubidium atoms into the highly fine cavity of the MPQ experiment results in an increase in the transmitted power, which triggers a feedback switch that increases the power to drive the laser (dashed line). This traps the atoms in a light field that contains an average of one photon, and the atoms stay in the cavity for up to 17 ms;After 3 milliseconds, the laser light intensity returns to its initial value, waiting for the next atom**. The large oscillation of the transmitted light power reflects the motion of the captured atoms. In Caltech experiments, these oscillations are more regular, indicating that the motion of the atoms is more periodic.
Cavity-mediated cooling is interesting because it complements other recently developed techniques for capturing molecules.
However, in addition to changing the strength of the intracavity field, atoms that periodically exchange energy with the cavity can cause rapid fluctuations in the amplitude and phase of the light field. Since the trapping potential is determined by the light field inside the cavity, these changes cause fluctuations in the light force. These fluctuations, in turn, affect the momentum of the atom in a random way, usually by increasing the velocity of the cold atom to heat it.
A distinctive feature of the cavity-QED scheme is that even if there is only one photon in the cavity, the depth of the well is large enough to accommodate a laser-cooled atom. Since the electric field of each photon is large, so is the light force of each photon, so a single photon can be captured in a small cavity.
But to trap atoms in the photon dipole potential, there is one more trick involved: the electric potential cannot be turned on until the approaching atoms reach the center of the cavity. Otherwise, an atom that falls into a trap from one side will escape from the other, just as a marble rolled into a bowl will roll out again without being caught.
Since we can now observe the position of atoms in a cavity field that contains less than one photon on average, we can turn on the electric potential at the right moment.
When atoms enter the cavity, they cause an increase in the transmission of light from the external laser, which triggers a switch that increases the power to drive the laser. If the timing is right, the atom will be on the opposite node of the standing wave dipole potential for several milliseconds – about ten times longer than if it were not switching.
The large oscillations that are evident in the transmitted intensity reflect the motion of the trapped atoms. In particular, when the atoms are in the center of the cavity, the transmittance is high, and when the atoms are far away from the axis of the cavity, the transmittance decreases.
At first glance, capturing atoms with a single photon in a cavity may seem similar to trapping atoms with a laser beam in free space;The difference is that the increase in intensity in the cavity allows us to use a weak laser. However, the strong coupling of atoms to cavities requires a conceptually different description, which we can understand by borrowing a simple ** from chemistry.
Atoms in action. Reconstructed trajectories of individual atoms measured in Caltech experiments. Since the cavity is smaller, the atoms are coupled to the cavity correspondingly, resulting in a regular trajectory (green). After falling into the cavity from above, the atom rapidly orbits around the high-intensity region (red) in the center of the anti-node in a plane perpendicular to the axis of the cavity;The period of motion is about 150 microseconds, and the time that atoms stay in the cavity is about one millisecond.
Just as two protons in a hydrogen molecule can be surrounded by a symmetric (i.e., combined) or antisymmetric (anti-bound) electron wave function, in an atomic-cavity system, the atomic dipole moment can oscillate in phase (combined) or out of phase (anti-bonding) with the light field.
Both states of atom-cavity "molecule" contain a quantum of energy, which can oscillate between atoms and holes. Thus, this quantum is shared by atoms (excited as electrons) and holes (as photons), just as electrons in a hydrogen molecule are 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 prolongs the residence time of the photon in the cavity.
Atomic physicists can now inversely calculate the classical trajectory of atoms by measuring the light passing through the cavity. This is possible because the transmitted light depends on the coupling between the atom and the cavity, which in turn depends on the position of the atom.
In the Caltech experiment, the huge atom-field coupling strongly confined the atom to an anti-node, so its motion was mainly confined to a plane perpendicular to the axis of the cavity. This movement is expected to be regular, with little perturbation of spontaneous radiation.
Thus, we can assume that the angular momentum of the atom around the axis of the cavity hardly changes during one revolution, and the conservation of angular momentum means that we can determine a constant of motion.
In addition to the sign of angular momentum and the specific anti-node on which the atom is located, the two-dimensional orbit can be reconstructed from the data by an algorithm based on the classical equations of motion. The reconstruction algorithm has been tested by applying the signals obtained by simulating the motion of atoms. In fact, Caltech's Christina Hood and her collaborators have found that the spatial resolution of such inferred trajectories is typically around 2 microns on a 10-microsecond time scale.
The research team at MPQ also conducted simulations to explore the movement of atoms in cavities. In MPQ experiments, the capture potential is weaker, so the atomic motion is more perturbed by spontaneous radiation.
Simulate motion. Simulating the movement of atoms in cavities, in the MPQ experiment, the coupling between atoms and the light field in larger cavities is relatively small, which increases the effect of momentum shocks from spontaneous radiation events. These momentum disturb the otherwise regular motion of the atoms in a plane perpendicular to the axis of the cavity, making the atomic trajectories (yellow) more random. Atoms enter from below and get about 12 ms.
Atomic transitions. The fluctuating electric potential increases the velocity of the atoms, while the cavity-mediated friction decreases the velocity of the atoms. In this case, the atom can leave one anti-node (denoted by a horizontal line), fly along the axis of the cavity, and then be recaptured by another anti-node. According to the simulation, this atom has flown over two anti-nodes in a row. Before and after the flight, the captured atoms swing rapidly around the associated anti-nodes. The periodic bursts of photons observed in the light transmitted through the cavity can prove that the atoms have made a long flight.
The simulation results also show that the captured atom sometimes flies towards another distant anti-node, making the motion a true three-dimensional motion. This movement is caused by two different but equally important mechanisms. First, the atoms are heated out from an anti-node due to the fluctuation of the capture potential. Then, as the cavity-mediated friction (proportional to the atomic velocity) cools the moving atoms, the atoms are trapped in another counternode.
Experimental evidence for the long-distance flight of atoms comes from the measurement of fluctuations in the intensity of transmitted light in cavities. When the atom is close to the anti-node, the transmittance is larger, whereas when the atom is close to the node, the transmittance decreases, providing valuable information about the position of the atom. In particular, atoms moving along the axis of the cavity periodically modulate the transmittance.
In general, the transmission strength is unstable, but occasionally there are periodic oscillations and then it becomes random. According to the explanation of this behavior, each peak in the light intensity is due to the strong coupling of the atom with each anti-node it passes through until it stabilizes at a distant anti-node.
The techniques that allow us to measure the trajectories of atoms in cavities can also be used to study the dynamics of single molecules when chemical reactions or biological processes occur.
Another exciting possibility is to expand the technology developed in different areas of science and engineering, i.e. to monitor the state of the system and apply appropriate feedback loops to control the state. For example, chemical reactions can be coherently controlled with appropriately tailored ultrashort laser pulses. These pulses are optimized in successive experiments, but are always applied to molecular systems prepared in the same way.
However, a new generation of atomic cavity experiments allows us to repeatedly study feedback loops applied to the same system, without having to prepare the system in the same initial state for each experiment. In addition, this feedback experiment also provides us with an exciting possibility, namely:The motion of atoms in the cavity can be precisely controlled according to the laws of quantum mechanics
Feedback experiments may also cool the atoms in the cavity to low temperatures. By applying a corrective force to atoms – a variant of the "random cooling" technique developed to cool particles stored in high-energy accelerators, we may be able to cool atoms to areas where the quantum mechanical properties of atomic motion become important.
At this stage, atoms can no longer be seen as point-like particles moving along classical trajectories. Instead, it must be seen as a wave packet that can be continuously observed in space. According to Heisenberg's uncertainty principle, the momentum of the wave packet changes every time we locate an atom. This measurement of quantum limits will be a challenge for future experiments.
Another interesting situation arises when two or more atoms are present in the cavity at the same time. In this case, the photons emitted by one atom are stored in the cavity, absorbed by another atom, and then re-emitted into the cavity to be reabsorbed by the first (or even third) atom. Therefore, atoms are not independent of each other. Conversely, the common field in the cavity establishes a long-range interaction between the atoms, so a synergistic effect can be expected from the motion of multiple atoms. For example, when an atom moves from an anti-node to a node, if the field in the cavity is opened, then it will affect the motion of the other atoms.
Systems where one or more individual atoms are at rest and strongly coupled to a single mode of the electromagnetic field are ideal for testing fundamental concepts in quantum computing and quantum information processing.
In fact, Scott Parkins, now at the University of Auckland, and collaborators at the JILA Lab and Caltech in Boulder, Colorado, first proposed the system as an efficient quantum interface in 1993. Using the strong coupling of atoms to single photons, it should be possible to map stationary qubits in the atomic medium to the propagating light field and vice versa. In other words, this scheme can send quantum information from one place to another.
In addition, the two atoms in the cavity can implement a "controlled NOT gate" – a fundamental building block of a quantum computer.
Cavity-QED experiments with individual atoms and optical photons will certainly provide a wealth of physics data for many years to come, and may initiate a large number of future applications in the field of physics and life sciences.
Because of this, quantum mechanics is bound to have a bright future for many years to come.