Two-wire guides and traps with vertical bias fields on atom chips

We present atom chip traps and guides created by a combination of two current-carrying wires and a bias field pointing perpendicular to the chip surface. These elements can be arranged in any orientation on the chip surface. We study loading schemes for the traps and present a detailed study of the guiding of thermal atomic clouds in an omnidirectional matter waveguide along a $25\text{−}\mathrm{mm}$-long curved path at various atom-surface distances $(35–450\mu \mathrm{m})$. An extension of the scheme for the guiding of Bose-Einstein condensates is outlined. Such a concept enables utilizing the full two-dimensional surface of the chip.

Figure 1

The upper row presents the potential for a one-wire side guide generated by a single wire on the chip surface and an external bias field (a) parallel and (b) perpendicular to the atom chip. The lower row presents the field configuration for a two-wire guide with (c) parallel currents and no bias field and (d) counterpropagating currents and an external bias field perpendicular to the plane containing the wires.

Figure 2

Equipotential lines for the magnetic potentials in a two-wire guide with counterpropagating currents and bias fields orthogonal to the wire plane, with different field strengths. In (a) the position of the wires and the direction of the currents is shown. (a), (b) For $B_b<B_{\mathit{crit}}$ one finds two guides above each other, one above and one below the plane of the wires. These two combine at $B_b=B_{\mathit{crit}}$ (c) and then split up into two side guides in the plane of the wires for $B_b>B_{\mathit{crit}}$ (d).

Figure 3

Time sequence over one oscillation period of a time orbiting guiding potential. Top: the magnetic field of the guide is shown in a plane perpendicular to the two wires. The direction of the wire current is indicated by the dot and cross, and its magnitude corresponds to the size of the symbols. The dashed lines indicate the position of the minimum of the trap in the static case. Bottom: each of the counterpropagating currents (solid and dashed curves) in two parallel wires is sinusoidally modulated around the steady current $I_0$. A relative phase difference of $\Delta \varphi =\pi ∕2$ results in a quadrupole field zero circling around the minimum of the static situation. With a proper choice of the modulation frequency, cold atoms are trapped in the time-averaged potential. While the position of the potential minimum remains unchanged with respect to the static case, the atoms never encounter a magnetic field zero and thus do not undergo Majorana spin flips.

Figure 4

(Color online) Numerical calculation of the TOP for the $d=h$ case for $I_{\mathrm{mod}}∕I_0=15\%$ [red (online)/dark gray (print)] and 30% [green (online)/light gray (print)]. The potentials are plotted versus the position perpendicular to the wires with respect to the guide’s minimum (left) and as a function of height over the wire plane (right). The length units are given in half wire separations $d$; the energy scale is given in units of the bias field $B$. Inside the circle of death, the potentials are depicted as thick solid lines, outside as dashed lines. For comparison, the harmonic approximation [Eqs. (7, 9)] (dotted lines) and the static potential (black lines) are shown.

Figure 5

(Color online) Deviations of the radius of the circle of death from Eq. (8) (solid line) in a full calculation. The dashed lines show the maximal and minimal distances of the field zero from the (average) potential minimum as functions of the current modulation $I_{\mathrm{mod}}∕I_0$. In the inset all positions of vanishing field are plotted (dashed lines) for the two cases $I_{\mathrm{mod}}∕I_0=15\%$ [red (online)/dark gray (print)] and $I_{\mathrm{mod}}∕I_0=30\%$ [green (online)/light gray (print)]. For comparison, the circles with the radius $r_0$ taken from Eq. (8) are shown (solid lines). The wire positions on the chip surface (black line) are marked as black solid circles; the length scales are given in units of the half wire separation $d$. The guiding potential minimum (both for the static and the TOP case) is marked as a black cross.

Figure 6

(Color online) Four different wire configurations for traps with vertical bias fields. (a) A guide created by two parallel wires is closed to form a trap by two crossing wires with antiparallel currents. (b) A similar trap can be built by two U-shaped wires. (c) Similar to (a), but the currents through the two closing wires are parallel in this case, which avoids the magnetic field zero at the trap minimum. (d) This wire configuration leads to a similar trap as the configuration shown in (c), also avoiding zero magnetic field, but without the need of crossing wires.

Figure 7

Equipotential lines (separated by $300\mu \mathrm{K}$ for ${}^7\mathrm{Li}$ in the ∣2,2⟩ state) for the magnetic potentials in a two-wire vertical trap as shown in Fig. 6a and different bias fields strengths (see text for other parameters). The potential barrier towards the chip vanishes for a bias field of $B_b⩾{\tilde{B}}_{\mathit{crit}}$ ($95\mathrm{G}$ for the given parameters).

Figure 8

Equipotential lines (separated by $300\mu \mathrm{K}$ for ${}^7\mathrm{Li}$ in the ∣2,2⟩ state) for the magnetic potentials in a two-wire vertical trap as shown in Fig. 6c and different bias field strengths $(I_w=2\mathrm{A})$.

Figure 9

(Color online) Chip design: Left: schematic drawing of the spiral-shaped wire. The black and gray lines indicate current-carrying wires; the white areas are grounded parts of the chip surface. Top right: the design of the double-U traps. The gold is shown in gray and the $10\text{−}\mu \mathrm{m}$ gaps are white lines. The origin of the coordinate system used in the text is indicated by the cross. The two $45\text{−}\mu \mathrm{m}$-wide U wires are part of the spiral-shaped wire forming the omnidirectional guide. Bottom right: microscope image of a detail of the spiral-shaped wire. The $10\text{−}\mu \mathrm{m}$-wide gaps from which the gold has been removed to define the wires appear as dark lines.

Figure 10

Schematics of the currents in the silver U wire underneath the chip (thick line) and in the double-U wires from the vertical trap. In our setup the center of the silver U wire is $1200\mu \mathrm{m}$ below the chip surface. Two different loading geometries have been studied either using parallel currents (a) or antiparallel current (b) in the closest chip wire with respect to the silver U wire.

Figure 11

(Color online) Parallel loading of the $200\text{−}\mu \mathrm{m}$ vertical trap. Top left: time diagram of the currents and bias fields used in the loading process: $I_U$ is the current through the silver U underneath the chip; $B_x$ and $B_z$ are the magnetic bias fields in the $x$ and $z$ directions, and $I_{dU}$ is the current through the $200\text{−}\mu \mathrm{m}$-wide U wire $(\times 10)$. Left: $xz$ cut through the calculated potential at $y=0$ with equipotential lines separated by $k_B\times 400\mu \mathrm{K}$ (definition of the $x\text{−}y\text{−}z$ directions as in Fig. 9). Right: experimental fluorescence images of trapped atoms during the transfer in the $xy$ plane (frame size $2150\times 4730\mu {\mathrm{m}}^2$). The number of atoms is not proportional to the fluorescence intensity, since the trap parameters are changed during the transfer (see text).

Figure 12

Lifetime graphs of three-dimensional traps based on two counterpropagating currents in combination with a vertical bias field. Two different loss mechanisms can be distinguished in the time domain: An initial overexponentially fast process plays a role during the first $\sim 100\mathrm{ms}$; afterwards a slow exponential loss (time constant $1.6\mathrm{s}$, solid lines) stemming from collisions with the background gas dominates. Both the rate and absolute magnitude of the fast loss depend on the depth of the trapping potential while the vacuum limited loss does not. The data were taken for traps with depths of $k_B\times 1250\mu \mathrm{K}$, $950\mu \mathrm{K}$, $500\mu \mathrm{K}$ (triangles, circles, squares, respectively). The error bars indicate the fluctuations in the fluorescence light. Note that during the first decay the atom number is underestimated due to the fact that the thermal energy of the atoms is higher than their natural linewidth.

Figure 13

Width of the longitudinal Gaussian fluorescence light distribution from a trapped atomic cloud. Decreasing width indicates loss of hot atoms. See text for explanations.

Figure 14

(Color online) $400\text{−}\mu \mathrm{K}$ equipotential surface of the spiral atom guide with a current of $1\mathrm{A}$ and a vertical bias field of $7\mathrm{G}$. The inset shows the potential minimum for different magnetic bias fields ($2\mathrm{G}$, $7\mathrm{G}$, $15\mathrm{G}$, and $30\mathrm{G}$) at the beginning of the guide. The longitudinal magnetic gradient pushes the atoms into the guide.

Figure 15

(Color online) Loading of the spiral. Top left: time diagram of the variation in the currents and bias fields during the loading of the spiral guide. $I_U$ is the current through the silver U underneath the chip, $B_x$ and $B_z$ are the magnetic bias fields in the $x$ and $z$ direction, and $I_S$ is the current through the $45\text{−}\mu \mathrm{m}$-wide spiral wire $(\times 10)$. Middle left: equipotential surface at $900\mu \mathrm{K}$ for the trap with $18\mathrm{G}$ horizontal bias field $(t=-10\mathrm{ms})$. Bottom left: equipotential surface at $500\mu \mathrm{K}$ during the rotation of the bias field at $t=-4\mathrm{ms}$ (horizontal field $7.2\mathrm{G}$, vertical field $4.2\mathrm{G}$). The opening of the guide for atoms with $E>500\mu \mathrm{K}$ is evident. Right: atomic fluorescence pictures during the loading process for different times from $t=-10\mathrm{ms}$ until $t=0\mathrm{ms}$ (frame size $2580\mu \mathrm{m}\times 6450\mu \mathrm{m}$ in the $xy$ plane). The fluorescence signal represents the distribution of the atoms during the loading of the guide. The number of atoms is not proportional to the fluorescence intensity, since the trap parameters are changed during the transfer (see text).

Figure 16

Left: the one-dimensional atomic density profiles (solid curves) along the spiral-shaped guide are shown for different guiding times. A Monte Carlo simulation (dashed curves) is in good agreement with the observed propagation dynamics. The insets show corresponding fluorescence images of the atomic cloud. Right: velocity distributions of the atomic sample obtained by the same Monte Carlo simulation show a reflection of the propagating atoms at a potential barrier at the end of the guide (center of spiral). This reflection can be clearly seen in the fluorescence images of the atomic cloud (see insets).

Figure 17

Lifetime graphs showing a comparison between the lifetime of a three-dimensional trap (squares) and the guide (triangles) of approximately equal potential depth of $k_B\times 500\mu \mathrm{K}$.