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Lattice Perturbations Cause Disproportionate Effects
Trapped BECs Get Really Perturbed
Disproportionately Large Effects From Very Small Changes in Optical Lattice Characteristics
November 2008
(a) BEC atoms 20 milliseconds after release from trap and single lattice beam, V1. This and the other images are obtained by recording the light absorbed by the expanding atoms. (b) BEC atoms after release from trap and a weak beam V2, approximately 7% the power of V1. (c) The atoms after a combination of primary beam V1 and perturbing beam V2. (d) The atoms after a combination of V1, perturbing beam V2 and a second perturbing beam, V3. V2 and V3 are each about 3% the intensity of the primary lattice beam, V1. But the distribution is substantially different.
Click image for enlarged view.
JQI researchers have discovered a surprising phenomenon, akin to a phase transition, that occurs when atoms cooled into a Bose-Einstein condensate (BEC) are placed in an optical lattice produced by a single laser beam and then exposed to an extremely weak perturbation from one or more additional beams. The presence of the perturbing beam/s causes a dramatic change in the density distribution of the atoms in the BEC -- much more than would be expected from the small magnitude of the perturbation. The result provides a striking new insight into large changes in the ground state of a system due to a small amount of disorder.
“People are very interested in phase transitions, where the state of a system goes from one sort of behavior to another sort of behavior,” says Matthew Beeler, a graduate student supervised by JQI Fellow Steve Rolston. “What we’re studying [with BECs in lattices] is a transition from an extended state -- meaning that the density of the atoms is spread out -- to a localized state where the density is congregated in a few places.” That transformation, Rolston’s group found*, is controllable by varying the characteristics of the additional weak laser beam/s superimposed on the “primary” lattice beam.
Calculations of density distribution show how the extended single-lattice wave-function (top) may be altered so that density is localized at "beat" points (bottom) where the primary and perturbing lattices interfere constructively.
BECs can form when a group of trapped atoms is cooled to a fraction of a degree above absolute zero.
Confined in that condition, most of the atoms “condense” into the same, minimum-energy quantum state. The JQI group starts with a cloud of about 10,000 rubidium atoms in a high-vacuum trap that uses magnetic fields and gentle nudges from light beams to quiet the atoms until they eventually condense into a space approximately 10 micrometers wide (about one-tenth the width of a human hair).
The trap is constructed such that the BEC forms about 2 mm from a mirrored surface. The researchers then shoot a single infrared laser beam through the BEC. It strikes the mirror and reflects back on itself, forming a standing wave pattern.
The atoms in the BEC “feel” the differences in potential energy created by the lattice beam, and arrange themselves into a density pattern that minimizes the energy of the BEC-lattice system. For most beam strengths, if the lattice beam is slowly turned off, the BEC returns to its initial lowest-energy, “ground-state” configuration after a few millionths of a second.
ABOVE: Two small circular mirrors (not dusty when taking data) are placed underneath the vacuum chamber. Each transfers one of the perturbing beams, at slightly different angles, into the BEC area via windows at the bottom of the trap. The primary lattice beam enters from another direction.
LEFT: The lattice trap is suspended inside the high-vacuum chamber. The rubidium gas is cooled to near absolute zero and slowed by collision with specially tuned photons from beams of laser light that surround the atoms in six directions. The fastest-moving atoms are allowed to escape. The remaining atoms are confined in the desired location with magnetic fields produced by coils (reddish-orange in the photos above) on either side of the vacuum chamber. The resulting near-motionless cluster forms the condensate, which is held toward the bottom end of the trap shown at left.
All of that was fairly well known. What was not known, or even anticipated, was the peculiar behavior that results when a second, very weak, laser beam is added to the primary beam, “perturbing” the state of the system. (See figure at right.)
The second beam has basically the same wavelength as the primary. But it is projected in at an angle, so when the two beams overlap, their periods are substantially out of synch. As a result, their lattice structures are “incommensurate” -- that is, they are out of phase by an amount that cannot be expressed in a ratio of integers such as 4:3 or 10:9.
This imposed disorder prompts a drastic change in the cluster density pattern of the BEC atoms (see figure, page 1) that is far in excess of the result that would ordinarily be expected from the small extra energy in such a weak beam alone. Instead of being extended in space, the atoms become “localized” into separate clusters. Adding a second perturbing lattice changes the density distribution of the system yet again. Those disproportionate effects indicate that the perturbing lattices have had a considerable impact on the wave function -- the quantum-mechanical description of the overall state of the atom-and-beam system.
That impact is reflected in the time it takes the system to return to its initial condition. In both of the multi-beam incommensurate cases, when all the beams are shut off, it can take the BEC about 100 times as long to return to its ground state as it does when the lattice is produced by the primary beam alone. (As a practical experimental matter, however, the perturbed-lattice BEC actually never returns to its ground state because the time interval is so long that interactions between the rubidium atoms set in, and begin to have a large, irreversible effect on the state of the system.)
The experimental apparatus surrounds a high-vacuum chamber -- the gray t-shaped enclosure at center of photo -- that contains the ultracold rubidium atoms in a trap (shown on next page), with numerous ports for laser-beam inputs. After the lattice beams are slowly shut off and the trap is released, a camera mounted on the far side of the table records an image of light that passes through the expanding cloud of atoms, indicating areas of highest and lowest density.
Rolston’s group used theoretical equations to calculate the degree of alteration in the atoms’ density patterns that should occur under various scenarios. The predictions were a good match with the observations -- up to a point. But the experimental values began to diverge substantially as a second perturbing lattice was added to the original and as the power of the lattice beams was increased.
Of course, the density distribution in the tiny BEC cannot be observed directly. (A beam of light sent in to take a measurement would alter the system.) So the researchers use an indirect method: They turn off the lattice beams and the trap potential. As the atoms start to expand, a camera takes a picture of the atoms’ momentum distribution after 20 milliseconds. The distribution reflects the initial density arrangement in the trap.
The experiment illustrates the value of using arrangements of ultracold atoms to introduce controlled, reproducible degrees of disorder into a condensed matter system. Those effects are difficult to study systematically in other contexts.
“There’s always some amount of disorder in condensed matter systems,” Beeler says, and the sources may be hard to account for, owing to the numerous possible variables involved.
Atomic systems, however -- such as the arrangement in the lattice experiment -- have much less intrinsic disorder and permit specific kinds of manipulation and adjustment of single variables.
“The bridge between atomic and condensed matter systems,” he says, “is that we can model the atomic systems and put in controllable disorder. Whereas in regular condensed matter systems you can’t control your disorder.”
* “Adiabaticity and localization in one-dimensional incommensurate lattices,” E.E. Edwards, M. Beeler, Tao Hong and S.L. Rolston. Accepted at Physical Review Letters.
Quantum Dots in a Whole New Light
Quantum Dots in a Whole New Light
September 2008
JQI Fellow Glenn Solomon and JQI colleague Andreas Muller. The quantum dot is placed inside the liquid-helium cryostat (left) at 4.2K and excited with laser beams.
A team headed by JQI Fellow Glenn Solomon of NIST has reached a new milestone in understanding and manipulating the exotic creations called “quantum dots,” or QDs for short.*
QDs are artificial three-dimensional structures, made of semiconductor material, that are only a few tens of nanometers at their widest. That’s small: About 1,000 dots placed side by side would barely equal the width of a human hair. But it’s exactly the right size to perform certain kinds of tricks that are much in demand in nanoelectronics and information processing, as well as quantum optics and encryption.
In particular, researchers are interested in QDs’ ability to act like individual atoms, each of which has a strictly limited, clearly demarked set of permitted energy states -- and hence a very specific set of photon frequencies that it can absorb and emit.
Although QDs contain tens of thousands of atoms, they have some atom-like behaviors because of the peculiar nature of quantum-mechanical objects. In the quantum world, where particles can act like waves, each object (such as an electron) has an associated wavelength. Structures of the right size can confine a certain set of wavelengths just as a clarinet or oboe can play a certain set of notes whose wavelengths have the right mathematical relationship with the length of the horn. The longer oboe can resonate with longer confined wavelengths, and thus can play lower notes: Frequency depends on size. The same is true for quantum dots. And just as a musician can choose a particular instrument to play a desired set of notes, nanoscientists can customize dots for different purposes.
In the case of QDs, the wavelengths of interest belong to a two-part entity that behaves as a single “quasiparticle”: an electron and a "hole." (A hole is the absence of an electron in the semiconductor material's lattice that results when an electron is excited out of its ground state. Holes behave like, and can be treated as, positively charged objects.) The electron-hole pair is called, appropriately, an exciton because it can be viewed as an excitation in the crystal, and because they release energy in the form of a photon when they recombine. Additional quanta of energy can produce paired excitons, called biexcitons. Like every other quantum-mechanical entity, excitons and biexcitons have associated wavelengths. QDs are the right size to confine those wavelengths in three dimensions.
As a result, QDs promise to serve as a minutely controllable source of photons for signal processing, and for generating “entangled” pairs of photons to use in transmitting secure keys to encrypted messages. Dots produce a dependable volume of photons with a high degree of wavelength accuracy, and their semiconductor materials are familiar to scientists and engineers.
When excitons or biexcitons recombine, they emit photons or pairs of photons in a “radiative cascade,” dropping from one energy level to the next lowest as they shed energy. In the quantum world, only certain energy levels, or quanta, are permitted. So there are only a few allowed sequences, or paths, for this transition process, and each path results in emission of photons of particular distinctive wavelengths. There are parallel paths, with each path producing photons of opposite polarization. That could make them ideal subjects for entanglement because, in the absence of information about which photon was polarized in which direction, taking a measurement of one photon would instantly determine the other's polarization.
Exploiting those properties in a practical device, however, will require extremely sensitive understanding of exactly how QDs emit certain kinds of photons in specific conditions. So Solomon and colleagues set out to determine how completely the full emission spectrum of a QD could be controlled and measured.
Their technique involved two separate lasers trained on the dot. The first was used to "dress" the dot by using the stro0ng laser field to alter the quantum dot states. Then a second laser beam was applied to inject carriers into the QD states. As these carriers relax to lower energies, they emit photons of various particular wavelengths depending on which of the allowed pathways they followed..
The group made its QDs of indium arsenide embedded in a surrounding crystal of gallium arsenide. To minimize thermal “noise” effects, they cooled the sample to 4.2 degrees above absolute zero with liquid helium. Then they focused on emissions from a single “dressed” QD about 30 nanometers (billionths of a meter) wide and 5 nm high. If the control ("dressing") laser beam and the pump laser beam were in the same plane, optical "noise" from scattered control photons would ruin the output signal. So the team attached an optical fiber carrying the control beam at right angles to the pump beam. (See illustration.)
Under the experimental conditions, the QD exciton and biexciton states have five or 10 ways to emit photons of various wavelengths. By using different tunings of the lasers, the researchers were able to prompt and record every possible permitted emission from the dot, notably including the “fine structure” that is well known in theory, but difficult to observe. In all cases, the experimental data were in excellent agreement with simulations produced by theoretical calculations.
The work constitutes the first instance in which the complete exciton-biexciton emission spectrum of a dressed QD has been recorded. But it has considerable further significance, for two reasons. First, the group was able to produce any desired emission by controlling the intensity and “detuning” of the control laser. (Detuning is the process of shifting the frequency of one wave so that it is out of resonance with the target QD transition.) Whether this can eventually be accomplished in a practical device at room temperature is unknown. But if so, it could provide the basis for exquisite control over photons used in numerous forms of quantum information processing.
That sort of regulation could compensate for the inherent problems that arise when QDs -- which are often fabricated by spraying atoms onto a surface in a vacuum, a necessarily inexact method -- emerge with asymmetrical proportions that in turn affect their optical properties.
Second, the JQI group demonstrated that the output of the dressed QD could be generated one photon at a time by using a pulsed laser source for the pump beam. That ability will be important in any eventual functional equipment based on the phenomena.
In the next stage of the research, the group will tackle the problem of making photons using their optical techniques when the original QD asymmetries forbid them.
* "Emission Spectrum of a Dressed Exciton-Biexciton Complex in a Semiconductor Quantum Dot." Andreas Muller, Wei Fang, John Lawall and Glenn S. Solomon. Physical Review Letters 101, 027401 (July 2008).
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