An
optical lattice is formed by the
interferenceIn physics, interference is the addition of two or more waves that results in a new wave pattern.Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same...
of counterpropagating
laserA laser is a device that emits light through a process called stimulated emission. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses...
beams, which creates a periodic (in space) polarization pattern. The resulting periodic
potentialA scalar potential is a fundamental concept in vector analysis and physics...
can then be used to trap neutral
atomThe atom is a basic unit of matter consisting of a dense, central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s via the Stark shift. Atoms are cooled and congregated in the potential minima. The resulting system of trapped atoms resembles a
crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is crystallography...
in the sense that the atoms are in a periodical potential.
Because of quantum tunneling, atoms can move in the optical lattice even if the
wellA potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy because it is captured in the local minimum of a potential well...
depth of the lattice is higher than the energy of the atoms, which is similar to the
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
s in a
conductorIn science and engineering, an electrical conductor is a material which contains movable electric charges. In metallic conductors, such as copper or aluminum, the movable charged particles are electrons...
.
An
optical lattice is formed by the
interferenceIn physics, interference is the addition of two or more waves that results in a new wave pattern.Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same...
of counterpropagating
laserA laser is a device that emits light through a process called stimulated emission. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses...
beams, which creates a periodic (in space) polarization pattern. The resulting periodic
potentialA scalar potential is a fundamental concept in vector analysis and physics...
can then be used to trap neutral
atomThe atom is a basic unit of matter consisting of a dense, central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s via the Stark shift. Atoms are cooled and congregated in the potential minima. The resulting system of trapped atoms resembles a
crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is crystallography...
in the sense that the atoms are in a periodical potential.
Because of quantum tunneling, atoms can move in the optical lattice even if the
wellA potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy because it is captured in the local minimum of a potential well...
depth of the lattice is higher than the energy of the atoms, which is similar to the
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
s in a
conductorIn science and engineering, an electrical conductor is a material which contains movable electric charges. In metallic conductors, such as copper or aluminum, the movable charged particles are electrons...
. However, there will be a
superfluidSuperfluidity is a phase of matter or description of heat capacity in which unusual effects are observed when liquids, typically of helium-4 or helium-3, overcome friction by surface interaction when at a stage at which the liquid's viscosity becomes zero...
–
Mott insulatorMott insulators are a class of materials that are expected to conduct electricity under conventional band theories, but which in fact turn out to be insulators when measured...
transition if the
interaction energyIn physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being considered.The interaction energy usually depends on the relative position of the objects...
between the atoms becomes larger than the hopping energy when the well depth is very large. In the Mott insulator phase, atoms will be trapped in the potential minima and cannot move freely, which is similar to the electrons in an
insulatorInsulator may refer to: something with science* Insulator , a substance that resists the flow of electric current* Insulator , an element in the genetic code* Thermal insulation, a material used to resist the flow of heat...
. In the case of Fermionic atoms, if the well depth is further increased the atoms are predicted to form an antiferromagnetic, i.e.
NéelNeel may refer to:* Alice Neel film about painter Alice Neel* Neel, in Indian numbering system* Neel Kamal directed by Kidar Nath Sharma* Neel Kamal directed by Ram Maheshwari...
state at sufficiently low temperatures . Atoms in an optical lattice provide an ideal quantum system where all parameters can be controlled. Thus they can be used to study effects that are difficult to observe in real crystals. They are also promising candidates for
quantum informationIn quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...
processing.
There are two important parameters of an optical lattice: the
wellA potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy because it is captured in the local minimum of a potential well...
depth and the
periodicityPeriodicity is the quality of occurring at regular intervals or periods and can occur in different contexts:In timing devices:* A clock marks time at periodic intervals.* A metronome ticks at periodic intervals of time....
. The well depth of the optical lattice can be tuned in real time by changing the power of the laser, which is normally controlled by an AOM (
acousto-optic modulatorAn acousto-optic modulator , also called a Bragg cell, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves . They are used in lasers for Q-switching, telecommunications for signal modulation, and in spectroscopy for frequency control. A piezoelectric...
). The periodicity of the optical lattice can be tuned by changing the
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the laser or by changing the relative angle between the two laser beams. The real-time control of the periodicity of the lattice is still a challenging task. Because the wavelength of the laser cannot be varied over a large range in real time, the periodicity of the lattice is normally controlled by the relative angle between the laser beams. However, it is difficult to keep the lattice stable while changing the relative angles, since the interference is sensitive to the relative
phaseThe phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic...
between the laser beams. Recently, a novel method of real-time control of the lattice periodicity was demonstrated, in which the center fringe moved less than 2.7 μm while the lattice periodicity was changed from 0.96 to 11.2 μm. Whether this method can keep atoms (or other particles) trapped while changing the lattice periodicity remains to be tested experimentally. Such
accordionThe accordion is a portable box-shaped musical instrument of the hand-held bellows-driven free-reed aerophone family, sometimes referred to as a squeezebox...
lattices are useful for controlling ultracold atoms in optical lattices, where small spacing is essential for quantum tunneling, and large spacing enables single-site manipulation and spatially resolved detection.
Besides trapping cold atoms, optical lattices have been widely used in creating
gratingA grating is any regularly spaced collection of essentially identical, parallel, elongated elements. Gratings usually consist of a single set of elongated elements, but can consist of two sets, in which case the second set is usually perpendicular to the first...
s and
photonic crystalPhotonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons...
s. They are also useful for sorting microscopic particles, and may be useful for assembling cell arrays.
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