Tunnelling barriers may be used for atomic circuits atomtronics , e. High gradients may ensure guided propagation with less excitation to higher vibrational states due to imperfections and noise, and they may also enable reaching the Lamb-Dicke regime to the point of using side-band cooling for single atoms, recently achieved in a non-chip 3D optical lattice [ ]. Bringing cold atoms closer to surfaces offers an ever-widening variety of possibilities for applying the atom chip method to surface and solid-state science.
The investigation of topics such as Johnson noise, the CP force, surface quantum phenomena, and electron transport are being realized and are discussed in this section. In relation to close encounters with the surface, we also discuss the achievement of spin and spatial coherence, as well as work on the hypothesized fifth force. Additional topics, including plasmons, vortices and high- T c superconductors, as well as domain formation in exotic materials, have already been noted in Section 3. Even near-contact biophysical measurements may be projected for atom chips Section 6.
As atom traps are brought closer to the surface, the surface increasingly acts as a disruptive environment. The effect of noise on cold atoms in magnetic traps, due to technical sources and random thermally induced currents Johnson noise , has been theoretically analysed in detail in [ 42 , 43 , 59 , 61 , ]. For neutral atoms, both sources of noise scale as d -2 for typical atom-surface distances d [ 21 , ] and may cause losses from atom chip traps due to spin-flip transitions when the noise frequency is on resonance , as well as heating due to position and frequency instability of the traps or guides [ 43 , 49 ].
Technical noise is the simplest form of disruptive noise, originating in the power supplies which drive the atom chip currents, or from electromagnetic noise that is picked up from the environment by the cables feeding the chip. By shifting the energy levels Zeeman shifts , technical noise at all frequencies may also cause spin decoherence. Technical noise has a long correlation length and is therefore not expected to give rise to spatial decoherence directly.
However, as shown in [ 50 ] in the context of atom—atom interactions, long correlation-length noise may cause spatial decoherence indirectly by giving rise to atom loss. Technical noise is typically the strongest type of noise encountered on most types of atom chips, except those with persistent supercurrents or with permanent magnets. Johnson noise is another type of noise.
Its origin lies with virtual electron currents due to thermal energy. Johnson noise becomes progressively more important relative to technical noise as atoms are brought closer to the surface; at small distances the power requirements are much lower and this typically enables the use of ultralow-noise current sources.
The first experimental study of this noise in atom chips was done by the Hinds group [ 19 ]. A systematic experimental study of the difference between the magnitude of Johnson noise and technical noise was done in [ 21 ]. Superconducting surfaces are expected to have very low levels of noise [ 56 , , , ] and this has indeed been confirmed by experiments measuring the effect of noise on spin-flips [ , ]. Probing Johnson noise and the CP potential on a chip. Line C is the measured contour line of 22 ms lifetime near the metal.
The solid dashed lines are calculated with without CP potential for the condensate, 2. Johnson noise may also be minimized using materials with lower conductance for the nearby surface, as accomplished with permanent-magnet chips. Thinner conducting layers reduce Johnson noise through the use of less material, which may also be achievable with CNTs or nanowires. Additional proposals have also been made for using exotic materials such as electrically anisotropic conductors [ 61 ], or by utilizing alloys at low temperatures [ 59 ], as noted in Section 3.
Electric fields caused by surface chemistry are also of great concern, especially for ultracold Rydberg atoms. Patch potentials forming DC fields have recently been analysed experimentally by the Dumke group using Rydberg atoms as sensitive probes [ 90 ]. Disruptive fields in the DC domain may also be caused by magnetic impurities as well as by scattered electron currents from rough wire edges, polycrystalline domain walls and internal geometric imperfections or material impurities.
Such fabrication imperfections can become especially damaging at small atom-surface distances and may cause potential roughness, thereby damaging or destroying the desired trapping or guiding of atoms. In the early days of the atom chip, these static magnetic fields sometimes became strong enough to cause breakup of the ultracold atomic cloud. It has been further characterized by many subsequent studies [ 19 , 44 , , ] and is reviewed in [ 16 ].
Several ideas for combating such effects have arisen, including time-dependent potentials suggested by the Westbrook and Bouchoule group [ ]. Fragmentation effects may be somewhat overcome by using more advanced and careful fabrication techniques, such as those reviewed in [ ].
Further progress is still required. For example, it has been shown that significant effects come from internal bulk scattering [ 45 ]. It would be interesting to check if single-crystal gold exhibits the same magnitude of internal scattering. Similarly, it would be interesting to check other crystalline materials such as CNTs and graphene. The recent advent of spatial interferometry close to the surface [ ] could enable the measurement of correlation lengths, a topic of considerable interest extending beyond atom optics on atom chips.
For example, what is the actual correlation length of Johnson noise? Is it on the same order as the distance to the surface — as predicted [ 43 ] but never measured directly? Similarly, what is the correlation length of the current shot-noise? There are many other interesting noise sources to be studied, another example being the noise peak produced by superconductors at T c [ , ]. One of the major challenges of atom interferometry with magnetically sensitive atoms is the preservation of coherence. This problem increases when trapping and manipulating the atoms very close to the chip surface.
Decoherence mechanisms, e. Diffraction has been observed for atoms dynamically reflected from close encounters with surfaces [ , ], but the atoms were not trapped by the atom chip potential. Theoretical understanding of spatial coherence in a BEC trapped in a confined configuration would involve both the effects of atom—atom interactions, which may be the major limitation in systems at large distances from the surface of the chip, and the effects of external noise.
These effects are usually non-additive and the interplay between them may yield counter-intuitive results. A discussion of this interplay in the context of atom chip interferometry has recently been presented [ 50 ]. Using a double-well model, it was shown that interactions may partially suppress decoherence for external noise causing phase fluctuations between the two wells. For external noise causing atom loss with relative number fluctuations however, as is likely the case in the spatial coherence experiment, decoherence may be enhanced by the atom—atom interactions. However, the interplay of these effects during a non-adiabatic time evolution has yet to be investigated.
All these factors affecting coherence are also highly relevant for the field of atomtronics. Pioneering experiments measured losses from a thermal-energy atomic beam of Na passing through a parallel-plate cavity at distances of 0. These phase shifts have been measured interferometrically in experiments sensitive to the non-retarded regime [ , ]. Probing the CP force by balancing evanescent-wave and surface potentials has been refined considerably using ultracold atoms [ , ]. In the first of two experiments conducted by the Zimmermann group, the position of the potential barrier is adjusted from to nm by varying the laser power.
Reflection probabilities are then measured for a range of initial velocities, controlled by switching magnetic potentials, that span a range from complete reflection below the classical barrier to complete transmission above it, the latter corresponding to complete atom loss. Quantum reflection discussed at the end of this sub-section is negligible for the velocity range chosen. Because the evanescent field can be accurately characterized, these experiments provide direct measurements of the CP force without requiring assumptions about the potential shape.
The results suggest that the best agreement is reached with a full quantum electrodynamics calculation of the force [ ]. The second of these experiments refined the surface to include an overlayer of parallel stripes of gold, adjacent to which the CP force is maximal due to the absence of the evanescent wave.
The surface therefore acts as a diffraction grating for a BEC incident at 3. The data analysis explicitly accounts for the lateral periodicity of the potential, enabling a significant advance in our understanding of how CP forces are modified by surface structures [ ]. It should be noted that these experiments have been extended by the same group, again using only optical and CP forces emanating from the surface, to the coupling of ultracold atoms and surface plasmons [ , ] see Section 3. Ultracold atoms brought close to the surface of an atom chip using purely magnetic potentials provide a potentially ideal platform for measuring CP interactions in the 0.
While the CP potential can destroy the trap at short atom-surface distances, it also affects the trap at larger distances. To quantify this weak effect at large distances, sensitive measurements of the trap frequency can be made as a function of the atom-surface distance [ 23 ]. Both sets of results agreed very well with theoretical predictions based on the substrate being at the same [ ] or elevated [ ] temperatures relative to the environment.
The agreement between theory and experiment is particularly impressive as it was obtained with no adjustable parameters. Probing the temperature dependence of the CP force. The fractional change in the trap frequency due to the CP force is shown as a function of the distance to the chip. Three sets of data are presented, with accompanying theoretical curves having no adjustable parameters. Error bars represent the total uncertainty statistical and systematic of the measurement. Atom losses caused by attractive forces between the atoms and the CNT were measured and used to characterize the atom-CNT interaction.
In a related implementation, cold atoms were used in a scanning probe microscopy configuration to measure CNT surface structures [ ]. In addition, because the BEC and the nanotube are comparable in size and mass, it may be possible to use the atoms to cool the nanotube, leading ultimately to its vibrational ground state [ ]. Probing dispersion forces using a chip-mounted CNT. The vertical dashed line indicates the position of the CNT tip.
The red shaded area denotes the regime where the condensate is in partial overlap with the CNT. Detailed features of CP forces continue to be investigated intensively including, for example, the influence of surface geometry e. Experimental and theoretical work has however, been much more extensive for Casimir forces than for CP interactions for a review, see [ ] , largely related to searches for repulsive Casimir forces that would allow, for example, the construction of frictionless MEMS devices.
Casimir forces have been demonstrated to be very dependent on surface geometry, and measurements show significant deviations from a pairwise additive formalism [ ]. Structured materials including metamaterials and layered substrates have been shown theoretically to exhibit tunable Casimir forces, including repulsion [ — ]. Repulsive Casimir forces have been measured experimentally, but only with a very specific choice of materials and a liquid medium [ ]. It remains to be seen what kind of manipulations of the CP force are possible through geometry and materials on the atom chip [ — ].
Intimately related to the CP attractive potential is the phenomenon of quantum reflection. As an atom approaches a surface, its classical trajectory simply accelerates towards the surface until the atom is either adsorbed or reflected by repulsive forces operating at the atomic-scale distances of surface chemical potentials.
Quantum mechanically however, if the atom is moving sufficiently slowly, the CP potential can instead cause reflection at much larger distances, with a probability related to the abruptness of the attractive potential [ ]. Quantum reflection can be firm but gentle, not even disrupting the extraordinarily fragile bond of He 2 [ ]. These reflection characteristics may also be relevant for experiments on antimatter [ ] Section 2.
Quantum reflection may be used to study CP interactions with different surface configurations. A recent suggestion for introducing atom chip technology envisions periodically doping the surface; the electric field generated by the surface dopants provides a force in addition to the CP interaction that can locally suppress quantum reflection [ ]. The surface, though flat, then acts as a diffraction grating for matter waves and may even be extended to realize further atom optics with flat substrates.
Here we briefly describe electron transport, a fundamental topic in solid-state physics, as a specific example of surface probing accomplished with atom chips. Several additional prospects for interactions with nearby surfaces, including hybrid devices and quantum surfaces, have been discussed in Section 3. This exceeded by three orders of magnitude anything expected from the conductor itself, whose structural spatial correlations are no longer than a few tens of nm typical of the grain size. This is a good example of how cold atoms in the vicinity of a surface may act as a novel probe.
An additional suggestion for cold-atom microscopy of electron transport in topological insulators has been proposed in [ 46 ]. Probing electron transport with cold-atom magnetometry on a chip. These fluctuations are due to variations in the direction of the current flow, nominally along the x axis. Different types of electron transport microscopy probes based on cold atoms could address many interesting questions. For example, can one detect and characterize different current regimes, e.
Can one detect andcharacterize non-classical currents, e. Or relativistic corrections [ ]? In addition, better understanding of electron transport may enable completely new types of conductors for atom optics on atom chips, as discussed in Section 3. Ultracold atoms are used to measure gravitational acceleration g and the universal gravitational constant G , with interferometric measurements yielding the highest accuracy and precision see, e.
Although these experiments do not use atom chips, the latter measurements in particular may soon be conducted in microgravity environments, for which the compactness afforded by atom chip-based platforms is crucial for experimental implementation [ 10 , 11 ]. Such microgravity experiments are also designed as tests of fundamental physics such as the Weak Equivalence Principle.
Most experimental work to date has been based on the use of a vertical optical lattice, typically created by retro-reflecting an off-resonant laser from the atom chip surface [ , ]. A variety of methods, using optical tweezers for example [ ], have been proposed to place the atoms into just one particular lattice site, with a known location.
The laser is then displaced to move the trapped cloud laterally over different regions of the atom chip, which is structured as a layered sandwich of metals with different densities. The gravitational field strength emanating from the surface is then a periodic function of the lateral position of the atoms. Useful strategies for minimizing limitations imposed by surface patch potentials have also been discussed [ ].
Probing the surface for non-Newtonian gravitational effects. An optical lattice is used to position cold 88 Sr atoms near two adjacent test masses. The width of the arrows represents the relative intensity of laser beams. Alternatively, magnetic potentials from the atom chip may be used to prepare and transport atoms and, in particular, to bring them close to the surface for initial loading into an optical lattice integrated into the atom chip Section 6.
Although these proof-of-principle experiments [ , ] do not state the atom-surface distances achieved, they may in the near future enable precision measurements of atom-surface interactions and other short-range forces. As discussed above, a multi-layer hybrid atom chip was used to magnetically transport cold atoms to the vicinity of a microcantilever [ ] Section 3. Pure magnetic traps may also be used for the complete experiment. As noted, the state-of-the-art for such traps stands at nm [ 20 ], and analyses of nanowire and CNT traps [ 60 , 62 , , ] suggest that even smaller distances may be achieved.
An alternative orientation of an atom chip has been proposed for measuring short-range interactions with a nanosphere [ ]. Orienting the atom chip vertically, the optical lattice may be created by a retro-reflecting laser aimed horizontally. The test mass consists of alternating vertical stripes behind the vertical wall of the atom chip; the ballistic trajectory of the falling nanospheres then depends on the density of the stripe closest to its initial position.
An interferometric scheme is expected to improve the sensitivity of the ballistic experiment. This scheme may also be applicable for measuring falling atomic trajectories adjacent to alternating gravitational fields. For completeness, we note here that a variety of experiments reviewed, e. Combined with the gravitational gradient, the optical lattice produces a Wannier-Stark potential manifold, allowing very long-lived Bloch oscillations to be observed.
This has improved the precision for corresponding measurements of g [ — ], though not to the level achieved in the interferometric measurements referred to above. It remains to be seen if the atom chip can also contribute to improved limits for a variety of related searches, e. Accurate control of small distances and wavepacket size, as well as exotic surfaces e. In addition, measuring correlation lengths of different effects may be possible using wavepackets separated parallel to the surface [ ]. Atom interferometry on a chip is much younger and less mature than conventional free-space interferometry using atomic beams, fountains and more recently, BECs.
Nevertheless, its development offers many potential advantages for the future. Beyond the fact that atom chips provide a compact miniature platform for precise manipulation of atoms, they also provide a unique environment for new kinds of interferometric schemes, e. In addition to traditional applications such as measuring acceleration and gravitation, inerferometry with ultracold atoms near a chip surface allows precise measurements of atom-surface interactions and thorough investigations of the fundamental physics of a Bose gas as a many-particle system, e.
In this section, we review spatial interferometry, in which each atom is split into a superposition of two locations or two momenta. At the end of this section, we will also briefly mention some interesting recent schemes of interferometry with superpositions of internal or discrete motional levels that are not separated in space. Specific aspects of interferometry on atom chips have been discussed in previous reviews of atom interferometry [ , ]. Here we attempt to encompass most of the important aspects of this interferometry, with emphasis on new developments during the last few years and focusing on achievements and proposals for future advancement.
The first demonstration of spatial interferometry on an atom chip was the Michelson interferometer realized jointly by the groups of Cornell, Anderson, and Prentiss [ ].
The latter was formed by a tightly focused laser beam reflected by a pair of mirrors on the chip. The wavepackets propagated in the magnetic waveguide for up to about 10 ms , whereupon a Bragg pulse reversed their direction. They were recombined upon arrival back at the centre of the waveguide using a second pair of laser sub-pulses. The relative number of atoms in the output momentum components showed clear interference fringes as a function of the relative phase between the wavepackets, which was engineered by imparting an initial velocity to the atom cloud before the splitting.
The magnetic waveguide in this experiment is important for preventing the expansion of the BEC, which would occur if it was released into free space. An atom chip as a platform for BEC inteferometry has a few additional advantages even if the interferometric sequence itself is performed with a freely propagating BEC, including simple and fast BEC formation. The atom chip also enables better control of the BEC after it is formed in order to optimize its shape and expansion rate.
These advantages were exploited by the Rasel group in a device designed to perform interferometry in microgravity [ ]. Bragg interferometery in microgravity on an atom chip at the Bremen drop tower.
The remaining time before the capture of the capsule at the bottom of the tower is used for atom interferometry AI and imaging of the atoms. A second kind of interferometry, which is unique to atoms and has no direct analogue in light waves, is based on splitting a BEC in a double-well potential. Coherent splitting of a BEC in a double-well potential was first demonstrated using an optical potential [ ].
The first demonstration of coherent double-well interferometry on an atom chip was achieved by the Schmiedmayer group by a splitting scheme based on an adiabatic dressed potential of RF and static magnetic fields [ ]. The details of the potential depend on the specific form of the vectorial static and RF fields, which are determined by the current configuration on the chip.
The fringe patterns were repeatable deterministic , as shown by a very narrow distribution of phases over many experimental realizations i. The relative phase between the two condensates was locked at zero whenever the chemical potential of the BEC was larger than the barrier height. Non-random phase differences were maintained for up to 2 ms , during which time the phase spread broadened, as measured by decreased fringe contrast. It was suggested that this rapid loss of coherence was due to the finite coherence length of the quasi-1D BEC along the axial direction, and this was later investigated in a study of many-body effects in a 1D Bose gas [ 29 ].
Using their double-well interferometer, the Schmiedmayer group conducted additional studies of fundamental effects, such as relaxation and pre-thermalization in isolated quantum systems [ 30 ], as well as measurements of a variety of non-equilibrium effects in a 1D Bose gas [ 28 , 31 , ]. An interferometric measurement of a non-magnetic gravitational potential difference between the locations of the two wells was performed by the Hinds group [ ].
The phase of the observed interference fringes allowed the determination of the energy difference between the chemical potentials of the two condensates. The precision of this measurement was limited by the chemical potential uncertainty, which determines the coherence time due to phase diffusion about 10 ms in this experiment. This was shown to be directly related to number squeezing, as also found in [ ]. The experiment demonstrated a novel beam recombiner that does not require a long time-of-flight to read out the relative phase; the barrier is reduced non-adiabatically and the two condensates are allowed to overlap for a given time and then they are separated again.
The resulting population imbalance between the two wells is then proportional to the sine of the relative interferometric phase before the recombination. An RF potential Mach—Zehnder interferometer on an atom chip. The double-well method has so far been used mainly to explore many-body effects, but the fact that phase coherence can be maintained has yet to be exploited in practical interferometry.
Atom—atom interactions play a crucial role in interferometry with a BEC in a trapping potential, as discussed extensively in the literature. For example, in addition to the work discussed above, superfluidity and hydrodynamics in a Josephson junction of a BEC were studied experimentally in an RF dressed double-well potential on a chip [ ]. Theoretical studies of BEC coherence in a double-well potential typical of atom chips were performed using various approaches, including stochastic methods [ , ]. A theoretical study of a full interferometric process in a Mach—Zehnder configuration with interacting atoms [ ] examined the effects of number-squeezing on the phase stability, showing that the standard quantum limit SQL for phase sensitivity can be overcome and the Heisenberg limit reached.
Tunnelling barriers for splitting atoms on a chip by static magnetic fields created by current-carrying wires may have the advantage of better integrability with other atom chip circuits to be used as platforms for more complex interferometric schemes. This may make the potential sensitive to imperfections in the structure of the wire, Johnson noise, time-dependent fluctuations of the currents and environmental magnetic noise that is transmitted by the metallic wires on the surface, as discussed in Section 4. Splitting a BEC using the double-well potential of a static magnetic field on an atom chip was realized in [ ].
Interference fringes were observed, but the phase of these fringes was random. A static field double-well potential on an atom chip. I 2 , of opposite polarity, creates the barrier of adjustable height and also determines the spacing between the two resulting wells. This offers a method for studying topological effects in tunnelling.
Atom chip for a tight double-well potential. The harmonic potential dashed is modified by using blue a single central wire and green, red adding opposing currents in successive pairs of adjacent wires. A state-selective dressed potential is formed by applying an inhomogeneous on-chip microwave field somewhat detuned from a specific transition between two Zeeman sub-levels in two hyperfine levels [ ]. Interaction with the microwave field shifts the energy of the two coupled levels by an amount which is proportional to the intensity of the field AC Stark shift.
This creates an effective potential for the two levels, whose shape is determined by the intensity and may be either attractive or repulsive. One of the two states can be shifted by a dressed microwave potential or they may both be shifted by a different potential. A BEC on a chip was first split with state-selective potentials by the Treutlein group in order to create an entangled two-component BEC, allowing the SQL of interferometry to be overcome [ 32 , ]. Double well on an atom chip using potentials created by microwave co-planar waveguides CPWs. The Si experimental chip has two layers of gold wires separated by a thin polyimide layer, with CPWs on the upper layer.
It is glued and wire-bonded to an AlN carrier chip with a single gold layer. The three central wires red form a CPW. All wires including the CPW can carry stationary currents for the generation of static magnetic traps. The position of the minimum of the static trap is indicated by the black cross.
Absorption images of the adiabatically split BEC. Next, we discuss some recent proposals for spatial interferometry based on splitting by state-selective potentials. A scheme for a double-well beam splitter was proposed by the Reichel group and some of its components were demonstrated experimentally [ 65 ]. A two-photon Rabi pulse can be tuned to transfer the ground state of the single well to the ground state of the double-well potential with minimal excitation of other trap modes in the two wells.
A numerical simulation based on mean-field calculations showed a high splitting efficiency. It would be interesting to investigate the evolution of the many-body state during this splitting and compare it to the experimentally studied double-well systems discussed in Section 5. A scheme for a Sagnac interferometer for inertial sensing based on state-selective RF-dressed potentials for the two trapped clock states has been proposed [ 66 ].
It is based on quasi-adiabatic transport of the two states in two corresponding 3D harmonic traps, moving in opposite directions along a ring-shaped trajectory. The magnetic configuration for these potentials had been proposed earlier [ ], but the new proposal also investigates the dependence of interference visibility on the adiabaticity of the transport dynamics for a BEC as well as thermal atoms.
Another proposal for an interferometer based on state-selective microwave potentials was analysed in [ 67 ]. Symmetric splitting would be accomplished by two CPWs producing two different microwave near-field frequencies. This allows splitting a thermal cloud of atoms into two clouds at positions shifted symmetrically from the original position and then reversing the splitting process to get an interferometric signal.
A thorough analysis of this scheme shows that symmetry allows a high-contrast signal even for thermal atoms and that it is robust against magnetic field fluctuations. Robustness due to time-reversal symmetry was previously found in relation with guided atom interferometers [ 64 ] and will be further discussed in Section 5. However, it was predicted that coherent operation of such an interferometer would require extremely precise magnetic field gradients that were beyond reach [ ] and references therein.
Nevertheless, it was recently demonstrated by the Folman group that coherent Stern—Gerlach interferometry is possible for a BEC on an atom chip [ ].
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To the best of our knowledge, this is the first realization of a coherent spatial Stern—Gerlach beam splitter. An interference signal can be obtained either by bringing the two wavepackets back to the same point and recombining them in a similar beam splitter, or by stopping their relative motion and observing interference fringes once they expand and overlap, as was done in the actual experiment. A magnetic field gradient generated by a current pulse in a chip wire was used to create the differential potential gradient.
New schemes for recombination of the split wavepackets, such as using a second beam splitter based on the same principle, would allow future experiments to benefit from the high momentum splitting achieved. Compared to standard Stern—Gerlach interferometery, an important advantage of the FGBS for interferometry is that its output contains a superposition of pairs of wavepackets with an indistinguishable state, such that long-wavelength magnetic fluctuations in space do not affect the relative phase between the two paths. This makes interferometry with atoms split with the FGBS insensitive to stray magnetic fields during propagation through the interferometer arms, since the atoms are in a superposition of different spin states only during the very short time of the splitting.
On the other hand, momentum transfer by magnetic gradients cannot achieve the precision offered by splitting with optical beams and would therefore be more suitable for applications using an atom guide, where momentum precision may not be as crucial Section 5. It should be noted that the FGBS may be realized with various kinds of state-selective potentials: magnetic, electric or optical.
The main limitation of splitting based on magnetic field gradients is the shot-to-shot stability of these magnetic fields, which are determined by current instabilities in the wires. An improved scheme based on a three-wire configuration was implemented to reduce the phase accumulation during the splitting due to the quadrupole field. Clock interferometry on a chip. Optical density curves are data blue and fits red to a simple combination of a sine with a Gaussian envelope. The vertical axis z is relative to the chip surface. Adapted from [ 37 ], with permission by AAAS.
As mentioned in Section 5. One of the obvious applications of guided interferometry is an area-enclosing loop, which would enable Sagnac interferometry for inertial sensing of rotation. The sensitivity of such a Sagnac interferometer is proportional to the area enclosed by the interferometer loop, which would be small on an atom chip as compared to free-space implementations.
High sensitivity could be recovered however, by constructing a high-finesse loop that would enable the atoms to perform many revolutions. In addition, closed-loop interferometer configurations may have symmetry properties that allow a high interferometric sensitivity even for thermal atoms and in the presence of potential imperfections [ 64 ], as also shown for another symmetric interferometric scheme [ 67 ]. Prospects for guided closed-loop interferometry have encouraged several proposals for overcoming some major technical obstacles.
To the best of our knowledge, the first attempt to realize a guided Sagnac interferometer was done by the Prentiss group [ ]. One detailed proposal for a full scheme of a Sagnac interferometer with a BEC on a chip is based on optical Bragg splitting and a magnetic atomic guide generated by an array of three or four parallel current-carrying wires [ ]. The proposed magnetic guide would prevent perturbations caused by the input and output currents on the loop by exchanging the active wires during the round trip of the atoms in the loop.
Another suggestion for preventing the problem of input and output for the loop current is a superconducting loop that maintains a persistent current [ ]. Many very creative ideas frequently emerge, such as the recently suggested potential loop generated by the current in a single-layer Archimedean spiral of two interleaved wires [ ]. However, care has to be taken to ensure that the potential is completely smooth as any roughness, due for example to the current leads, would hinder the operation of the Sagnac interferometer. Adiabatic dressed potentials have also been suggested as a method to create a variety of shapes of traps and guides for ultracold atoms.
Designs of ring traps for atoms were suggested [ , — ] as loops for Sagnac interferometry as well as structures for studying superfluidity in confined geometries. Inductive dressed ring traps have also been suggested [ , ], as well as rings based on moving actuators [ ]. Ring traps have been loaded [ , ], but not on an atom chip. The Dance Off. Ally Blake.
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