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Hamlet Karo Avetissian. Quantum Information and Coherence. Erika Andersson. Yunquan Liu. Optical Binding Phenomena: Observations and Mechanisms. Jonathan M. In all cases a — c , both surfaces contribute to the spectroscopy signal. The two peaks appear around. The minima occur at resonance at the trap bottom.
The low high frequency wing of the lowest highest frequency spectrum correspond to the case a , the central wing corresponds to the case c. Data from LPL. For evaporative cooling it is generally desirable to start with a RF frequency resulting in resonances away from the location of the atoms, as in figure 11 a or c , and then adjust the frequency so that the evaporation resonance surface approaches the atoms. The second RF can then remove the most energetic atoms and cool the gas to very low temperatures: see for example [ 14 , 46 ].
One can also directly address the gap between the dressed states with a low frequency field. At the minimum point, this means applying a second RF field with a frequency equal to the Rabi frequency of the first RF field. In this situation, the minimum point of the trap is addressed and the atoms will empty out.
However, if the low RF frequency is somewhat above the Rabi frequency, evaporative cooling can be performed, as demonstrated in [ 10 ] and reported in [ 8 , 74 ]. Evaporation can be maintained by reducing the RF frequency to approach the Rabi frequency.
The low frequency resonance can be used for spectroscopy, as outlined in section 3. However, for evaporative cooling, rather than spectroscopy, it can be desirable to use a fairly strong second field to ensure the hot atoms are out-coupled adiabatically. Non-adiabatic transitions lead to the population of different states which either are not trapped or lead to collisional losses [ 36 , 43 ].
For the direct transition, where , the Rabi frequency is modified by an approximate factor [ 10 ]: thus the coupling is somewhat reduced and we note it is also optimal for aligned RF and static fields. Finally, we note that it is possible to perform evaporative cooling without a second RF field [ 75 ]. In this case we can use the fact that for a quadrupole field, and for RF linearly polarised in a horizontal direction, the Rabi frequency varies hugely around the resonant ellipsoid: there will always be locations around the circumference of the ellipsoidal surface where the Rabi-frequency vanishes.
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These locations are places where the dressed trap 'leaks', i. But since these 'holes' are located high up on the sides of the ellipsoid, at the equator for a horizontal linear polarisation, only the most excited atoms can reach the hole and escape. Thus, we can implement evaporative cooling using this feature, as was reported in [ 75 ], although this evaporation through two holes is expected to be less efficient than an evaporation through a whole resonant surface [ 76 ].
To adjust the cooling and reduce temperature the holes can be lowered by controlling the RF polarisation using elliptically polarised RF.
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We note briefly that the holes could also be closed by using a rotating circular polarisation [ 77 ] which is a variant of a TAAP, a time-averaged adiabatic potential, see section 4. This same kind of evaporation was used in a double well TAAP in [ 78 ]. Ring traps for atoms have considerable interest, for example, as a geometry for excitations and solitons in quantum gases [ 79 ], as a way of pinning a vortex [ 80 ], and as an instrument for Sagnac interferometry [ 81 ].
In this context atom chips are of interest because they may lead to the creation of compact devices. However, a conventional atom chip approach would be to create a circular waveguide based on steady currents and magnetic fields such as in [ 82 ]. This is based on the idea that with current flowing down several long parallel wires on a chip surface, a magnetic 2D quadrupole field can be created away from the chip surface [ 83 ].
To trap atoms in a circular waveguide, one simply bends the parallel current carrying wires into concentric loops. However, a weakness of the single circular magnetic waveguide is the end effects associated with how the currents are brought into and out of the waveguide loop [ 84 ]. The potential issues, where currents enter and exit a waveguide ring, include distortion of the circular symmetry and the introduction of local bumps or dips in the waveguide potential. In this section, and in section 6 , we will see a number of techniques using dressed atom traps that avoid this problem and create smooth and symmetric ring traps for ultra-cold atoms.
In Morizot et al [ 11 ] published a proposal for a ring trap for atoms based on the intersection of two types of potential for ultra-cold atoms. First, an 'egg-shell' potential from a 3D quadrupole magnetic field dressed to resonance is used. Since 3D quadrupole fields have an axis with higher gradient because of Maxwell's equations 3 , this steeper gradient is arranged to be vertical, so that in the x —y plane a circular cross-section is obtained. Then the egg-shell system is overlaid with a blue-detuned optical potential formed from vertical standing waves of light a 1D optical lattice.
The intersection of these two potentials forms a set of ring potentials, stacked above each other, with different radii, see figure 12 a. Blue-detuned light was proposed to exclude atoms from regions of light and reduce photon scattering in the trap. For practical values of parameters [ 11 ], the trapping frequency in the vertical direction optical confinement is higher than in the horizontal direction RF confinement.
Indeed, the frequencies can be sufficiently high to reach a low-dimensional regime for a 1D, or 2D, quantum gas. A simple loading scheme was proposed which involved starting with the dressed RF atoms in the egg-shell trap, applying the blue-detuned standing wave of light to trap the atoms in a plane at the bottom of the egg-shell, and then shifting the RF trap downwards in position to open out the ring [ 11 ]. This latter step can be accomplished by applying a bias field to shift the quadrupole field downwards.
The scheme was realised in [ 12 ], but with the standing wave of light replaced by two sheets of light. Reference [ 12 ] also demonstrated a novel variation of the loading scheme in which a blue detuned sheet is applied first before the RF radiation. This is used to push the atoms away from the zero region of the quadrupole trap as the RF is turned on.
The ring trapping scheme of [ 11 ] has also been realised with light sheets in [ 85 ]. A ring of atoms is confined by the RF egg-shell potential radially with minimum marked in green , and vertically by a blue-detuned optical standing wave shown in blue. Figure adapted from [ 11 ]. The different cases show different vertical bias fields which have the effect of moving the eggshell potential vertically, thus changing the ring diameter. Figure 12 b reproduced from [ 12 ] under a CC-BY 3. At the start of section 4 , we mentioned that conventional atom-chip ring traps, based on purely magnetic waveguides without dressing , can have issues with their circular symmetry and local bumps or dips in the waveguide potential where currents enter and exit the waveguide structure.
One approach to resolve this is to use induction methods see section 6. Another approach uses two-phase RF currents [ 15 , 69 ] to make 2D rings or tubes in 3D. Figure 13 a shows the chip with two RF wires on the underside. By adjusting the phase difference between the currents of the wires, the character of the proposed dressed trap can be changed significantly. The underlying magnetic trap is formed from DC currents in all three wires shown in figure 13 a with appropriate bias fields in the z and vertical directions.
The bias field in the z -direction ensures a functional magnetic trap in all three directions. The bias field in the vertical direction shifts the magnetic trap to the correct vertical position. When the currents are out of phase, there is either a trap not unlike the original magnetic trap, or a ring-trap in the 2D plane shown. In this latter case, the conventional orientation of atom chips horizontally, with the atoms underneath means that the 'ring' belongs to a vertical plane, a bit like a car tyre, i.
So, for the ring to be fully populated with atoms, it should either be very small, or there should be compensation of gravity from a Rabi coupling gradient [ 16 ], or an additional potential, such as an optical gradient or a tilt of the chip. The depth of the ring in the horizontal z -direction in figure 13 a is determined by the length of the current carrying wires on the chip and the method used to confine the atoms in the z -direction.
In [ 15 ] the confinement was proposed to be formed by shaping the RF wires and the width was just a micrometre or so. In general, there are limitations to this approach because large rings will require large currents to place the magnetic linear quadrupole away from the chip surface; the part of the ring near the chip surface may be influenced by significant deviations from quadrupolar due to the proximity of the three wires and the finite width of the nearest current carrying wire, changing the local magnetic field direction.