A quantum interference apparatus includes a space and an alkali-metal atomic cell. A static magnetic field having a specific direction and a specific intensity is applied to the space. The alkali-metal atomic cell is disposed inside the space. Alkali-metal atoms are encapsulated in the alkali-metal atomic cell. As a static magnetic field is applied to the alkali-metal atomic cell and excitation light having at least two different frequency components is applied thereto, a quantum interference state of the alkali-metal atoms is formed. Among the frequency components of the excitation light, a frequency component that participates in the formation of the quantum interference state is light containing linearly-polarized lights having the same polarization direction as each other. The static magnetic field applied to the space is adjusted so that fluctuations of a transition frequency between ground levels forming the quantum interference state with respect to the magnetic field is suppressed.

A quantum interference apparatus includes a space and an alkali-metal atomic cell. A static magnetic field having a specific direction and a specific intensity is applied to the space. The alkali-metal atomic cell is disposed inside the space. Alkali-metal atoms are encapsulated in the alkali-metal atomic cell. As a static magnetic field is applied to the alkali-metal atomic cell and excitation light having at least two different frequency components is applied thereto, a quantum interference state of the alkali-metal atoms is formed. Among the frequency components of the excitation light, a frequency component that participates in the formation of the quantum interference state is light containing linearly-polarized lights having the same polarization direction as each other. The static magnetic field applied to the space is adjusted so that fluctuations of a transition frequency between ground levels forming the quantum interference state with respect to the magnetic field is suppressed.

A resonator for coherent oscillator matterwaves (COMW) includes a cavity bound by reflectors. The reflectors are fields of light blue-detuned with respect to an energy-level transition of the rubidium 87 (.sup.87Rb) atoms that constitute the COMW. One of the reflectors is partially transmissive to that COMW can enter and exit the resonator. The COMW resonator can be used to stabilize a COMW oscillator much as an optical resonator can stabilize a laser.

In some variations, an interferometric frequency-reference apparatus comprises: an atom source configured to supply neutral atoms to be ionized; an ionizer configured to excite the neutral atoms to form ionized atoms; an ion collimator configured to form a collimated beam of the ionized atoms; probe lasers; and a Doppler laser configured to determine a ground-state population of the ionized atoms, wherein the atom source, the ionizer, and the ion collimator are disposed within a vacuum chamber. Other variations provide a method of creating a stable frequency reference, comprising: forming ionized atoms from an atomic vapor; forming a collimated beam of ionized atoms; illuminating ionized atoms with first and second probe lasers; adjusting the frequencies of the first probe and second probe lasers using Ramsey spectroscopy to an S.fwdarw.D transition of ionized atoms; and determining a ground-state population of the ionized atoms with another laser.

A tri-axial magnetic field correction coil includes a first coil group and a second coil group with respect to an X-axis direction that passes through a clock transition space in which atoms are disposed. The first coil group is a Helmholtz-type coil composed in a point-symmetrical shape around the clock transition space. The second coil group is composed in a point-symmetrical shape around the clock transition space with respect to the X-axis direction, and is a non-Helmholtz-type coil that differs from the first coil group in terms of coil size, coil shape, or distance between coils.

A tri-axial magnetic field correction coil includes a first coil group and a second coil group with respect to an X-axis direction that passes through a clock transition space in which atoms are disposed. The first coil group is a Helmholtz-type coil composed in a point-symmetrical shape around the clock transition space. The second coil group is composed in a point-symmetrical shape around the clock transition space with respect to the X-axis direction, and is a non-Helmholtz-type coil that differs from the first coil group in terms of coil size, coil shape, or distance between coils.

In a general aspect, a photonic crystal maser includes a dielectric body having an array of cavities ordered periodically to define a photonic crystal structure in the dielectric body. The dielectric body also includes a region in the array of cavities defining a defect in the photonic crystal structure. An elongated slot through the region extends from a slot opening in a surface of the dielectric body at least partially through the dielectric body. The elongated slot and the array of cavities define a waveguide of the dielectric body. The dielectric body additionally includes an input coupler aligned with an end of the elongated slot and configured to couple a reference radiofrequency (RF) electromagnetic radiation to the waveguide. The photonic crystal maser also includes a vapor or source of the vapor in the elongated slot and an optical window covering the elongated slot.

In a general aspect, a photonic crystal maser includes a dielectric body having an array of cavities ordered periodically to define a photonic crystal structure in the dielectric body. The dielectric body also includes a region in the array of cavities defining a defect in the photonic crystal structure. An elongated slot through the region extends from a slot opening in a surface of the dielectric body at least partially through the dielectric body. The elongated slot and the array of cavities define a waveguide of the dielectric body. The dielectric body additionally includes an input coupler aligned with an end of the elongated slot and configured to couple a reference radiofrequency (RF) electromagnetic radiation to the waveguide. The photonic crystal maser also includes a vapor or source of the vapor in the elongated slot and an optical window covering the elongated slot.

Vapor cells may include a body including a cavity within the body. A first substrate bonded to a second substrate at an interface within the body, at least one of the first substrate, the second substrate, or an interfacial material between the first and second substrates may define at least one recess or pore in a surface. A smallest dimension of the at least one recess or pore may be about 500 microns or less, as measured in a direction parallel to at least one surface of the first substrate partially defining the cavity.

Vapor cells may include a body including a cavity within the body. A first substrate bonded to a second substrate at an interface within the body, at least one of the first substrate, the second substrate, or an interfacial material between the first and second substrates may define at least one recess or pore in a surface. A smallest dimension of the at least one recess or pore may be about 500 microns or less, as measured in a direction parallel to at least one surface of the first substrate partially defining the cavity.