Anatom interferometer is a type ofinterferometer that uses the wave-like nature of atoms in order to produce interference. In atom interferometers, the roles of matter and light are reversed compared to thelaser based interferometers, i.e. the beam splitter and mirrors are lasers while the source emitsmatter waves (the atoms) rather than light. In this sense, atom interferometers are the matter wave analog ofdouble-slit,Michelson-Morley, orMach-Zehnder interferometers typically used for light.^[1] Atom interferometers measure the difference in phase acquired by atomic matter waves traversing different paths. Matter waves may be controlled and manipulated using systems of lasers.^{[2]: 420–1} Atom interferometers have been used in tests offundamental physics, including measurements of thegravitational constant, thefine-structure constant, anduniversality of free fall. Applied uses of atom interferometers include accelerometers, rotation sensors, andgravity gradiometers.^[3]

Interferometry splits a wave into a superposition along two different paths. A spatially dependent potential or a local interaction differentiates the paths, introducing a phase difference between waves. Atom interferometers usecenter of mass matter waves with shortde Broglie wavelength.^[4][5] Experiments usingmolecules have been proposed to search for the limits of quantum mechanics by leveraging the molecules' shorter De Broglie wavelengths.^[6]

Interference of atommatter waves was first observed byImmanuel Estermann andOtto Stern in 1930, when a sodium (Na) beam was diffracted off a surface ofsodium chloride (NaCl).^[7] The first modern atom interferometer reported was adouble-slit experiment with metastable helium atoms and a microfabricated double slit by O. Carnal andJürgen Mlynek in 1991,^[8] and an interferometer using three microfabricated diffraction gratings and Na atoms in the group aroundDavid E. Pritchard at theMassachusetts Institute of Technology (MIT).^[9] Shortly afterwards, an optical version of aRamsey spectrometer typically used in atomic clocks was recognized also as an atom interferometer at thePhysikalisch-Technische Bundesanstalt (PTB) in Braunschweig, Germany.^[10] The largest physical separation between the partial wave packets of atoms was achieved using laser cooling techniques and stimulated Raman transitions bySteven Chu and his coworkers inStanford University.^[11]

In 1999, the diffraction of C₆₀fullerenes by researchers from theUniversity of Vienna was reported.^[12] Fullerenes are comparatively large and massive objects, having an atomic mass of about720 Da. Thede Broglie wavelength of the incident beam was about 2.5 pm, whereas the diameter of the molecule is about 1 nm, about 400 times larger. In 2012, these far-field diffraction experiments could be extended tophthalocyanine molecules and their heavier derivatives, which are composed of 58 and 114 atoms respectively. In these experiments the build-up of such interference patterns could be recorded in real time and with single molecule sensitivity.^[13]

In 2003, the Vienna group also demonstrated the wave nature oftetraphenylporphyrin^[14]—a flat biodye with an extension of about 2 nm and a mass of 614 Da. For this demonstration they employed a near-field Talbot–Lau interferometer.^[15][16] In the same interferometer they also found interference fringes for C₆₀F₄₈, a fluorinatedbuckyball with a mass of about 1600 Da, composed of 108 atoms.^[14] Large molecules are already so complex that they give experimental access to some aspects of the quantum-classical interface, i.e., to certaindecoherence mechanisms.^[17][18] In 2011, the interference of molecules as heavy as 6910 Da could be demonstrated in a Kapitza–Dirac–Talbot–Lau interferometer.^[19] In 2013, the interference of molecules beyond 10,000 Da has been demonstrated.^[20]

The 2008 comprehensive review by Alexander D. Cronin, Jörg Schmiedmayer, andDavid E. Pritchard documents many new experimental approaches to atom interferometry.^[21] More recently atom interferometers have begun moving out of laboratory conditions and have begun to address a variety of applications in real world environments.^[22][23]

While the use of atoms offers easy access to higher frequencies (and thus accuracies) thanlight, atoms possess mass and move slower; thus they affected more noticeably bygravity compared to beams of light.^[24] In some apparatuses, the atoms are ejected upwards and the interferometry takes place while the atoms are in flight, or while falling in free flight.^[25] In other experiments gravitational effects by free acceleration are not negated; additional forces are used to compensate for gravity.^[26][27] These guided systems in principle can provide arbitrary amounts of measurement time, providedquantum coherence is preserved.

The early atom interferometers deployed slits or wires for the beam splitters and mirrors. Later systems, especially the guided ones, used light forces for splitting and reflecting of the matter wave.^[28]

A prototypical technique for atom interferometry involves splitting, reflecting, and recombining atomic matter waves using pulses of light. This technique is also called the Kasevich-Chu atom interferometer, named after the authors of the 1991 paper.^[29] This method employs counter-propagating beams of light that produce transitions between two quantumstates labeled${\displaystyle |0⟩}$ and${\displaystyle |1⟩}$.^[30] Both lasers are tuned off-resonance from the excited state by a frequency Δ to avoid resonantly exciting and heating the atoms.

In addition to changing the spin state of the atom, the counter-propagating Raman transition provides amomentum kick${\displaystyle \hslash {\overrightarrow{k}}_{eff}=\hslash ({\overrightarrow{k}}_2-{\overrightarrow{k}}_1)}$ to one of the components.^[30] In a spin–momentum basis, a pulse of Raman light interacting with an atom will transition between${\displaystyle |0,0⟩}$ and${\displaystyle |1,\hslash {\overrightarrow{k}}_{eff}⟩}$. Applying a${\displaystyle \pi /2}$ pulse (seeRamsey interferometer) light to${\displaystyle {\psi }_0=|0,0⟩}$ produces theentangled state${\displaystyle {\psi }_1=\frac{1}{\sqrt{2}}\left(|0,0⟩+|1,\hslash {\overrightarrow{k}}_{eff}⟩\right)}$.

The interferometer is formed by three Raman pulses in a${\displaystyle \pi /2}$–${\displaystyle \pi }$–${\displaystyle \pi /2}$ configuration separated by a common non-interaction time${\displaystyle T}$. This scheme is analogous to aMach–Zehnder interferometer for light, where the first pulse splits the matter wave to travel along two different trajectories, the second pulse reflects the packets back toward each other, and the final pulse recombines the matter wave. The measured state of the matter wave after the interferometer sequence depends on the total phase difference${\displaystyle \mathrm{\Delta }\phi }$ accumulated along the two different trajectories, yielding a final probability of being in one of the states as^[31]$${\displaystyle P=\frac{1}{2}\left(1-C\cos (\mathrm{\Delta }\phi )\right),}$$where${\displaystyle C}$ is the visibility or contrast of theinterferometer fringe. Since the matter wave is in free-fall with respect to gravity, the phase difference depends on thegravitational acceleration${\displaystyle g}$ as^[30]$${\displaystyle \mathrm{\Delta }\phi ={\overrightarrow{k}}_{eff}\cdot \overrightarrow{g}{T}^2+\mathrm{\Delta }{\varphi }_L,}$$where${\displaystyle \mathrm{\Delta }{\varphi }_L}$ is any additional phase difference of the Raman laser beam arising between the light pulses.^[32]

The sensitivity of the interferometer to gravitational or inertial forces depends on:

• The space–time area enclosed by the interferometer, which increases for larger${\displaystyle T}$.^[33]
• The relative phase stability of the counter-propagating Raman beams.
• The number of atoms in the cold, trapped ensemble that complete the interferometer. A larger fraction of participating atoms increases${\displaystyle C}$. Due to theDoppler effect, atoms with finite temperature may not experience exactly${\displaystyle \pi /2}$ or${\displaystyle \pi }$ Raman pulses.

Group	Year	Atomic species	Method	Measured effect(s)
Pritchard	1991	Na, Na2	Nano-fabricatedgratings	Polarizability, index of refraction
Clauser	1994	K	Talbot–Lau interferometer
Zeilinger	1995	Ar	Standing light wave diffraction gratings
Helmke Bordé	1991		Ramsey–Bordé	Polarizability, Aharonov–Bohm effect: exp/theo${\displaystyle 0.99\pm 0.022}$, Sagnac effect 0.3 rad/s/${\displaystyle \surd }$Hz
Chu	1991 1998	Na Cs	Kasevich–Chu interferometer Light pulses Raman diffraction	Gravimeter:${\displaystyle 3\cdot {10}^{-10}}$ Fine-structure constant:${\displaystyle \alpha \pm 1.5\cdot {10}^{-9}}$
Kasevich	1997 1998	Cs	Light pulses Raman diffraction	Gyroscope:${\displaystyle 2\cdot {10}^{-8}}$rad/s/${\displaystyle \surd }$Hz, Gradiometer:
Berman			Talbot-Lau
Mueller	2018	Cs	Ramsey-Bordé interferometer	Fine-structure constant:${\displaystyle \alpha \pm 2\cdot {10}^{-10}}$

A precise measurement ofgravitational redshift was made in 2009 by Holger Muller, Achim Peters, and Steven Chu. No violations of general relativity were found to7×10⁻⁹.^[34]

In 2020, Peter Asenbaum, Chris Overstreet, Minjeong Kim, Joseph Curti, and Mark A. Kasevich used atom interferometry to test theprinciple of equivalence in general relativity. They found no violations to about10⁻¹².^[35][36]

The sensitivity of an atom interferometer to external influences generally improves as the matter wave's separation time increases.^[34] High sensitivity free-fall interferometers hence require long drop distances. For example, the MAGIS-100 experiment atFermilab employs a 100 meter drop tower, aiming to detectgravitational waves and ultralightdark matter,^[37] which is known to interact with regular matter only via gravity.

Space-based atom interferometers may be more sensitive to weak gravitational waves than terrestrial observatories such asLIGO.^[38]

Atomic interferometer gyroscopes (AIG) and atomic spin gyroscopes (ASG) use atomic interferometer to sense rotation or in the latter case, usesatomic spin to sense rotation with both having compact size, high precision, and the possibility of being made on a chip-scale.^[39][40]

• Electron interferometer
• Ramsey interferometry

• P. R. Berman [Editor],Atom Interferometry. Academic Press (1997). Detailed overview of atom interferometers at that time (good introductions and theory).
• Stedman Review of the Sagnac Effect

• Interferometers

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