Atomic clock and coherence close to a chip surface

Figure 1: Atoms are magnetically trapped at a distance d of a few micrometers from the room-temperature chip surface.

Applications of atom chips lie in the area of miniaturized atomic clocks, portable interferometric sensors, and quantum information processing. The ability to coherently manipulate internal states of the trapped atoms is an essential prerequisite for these applications. Long coherence lifetimes of internal state superpositions are required. Atoms in chip traps, however, can potentially suffer from decoherence due to interaction of the atoms with the surface of the chip, in addition to other decoherence mechanisms which are also present in macroscopic traps. The chip surface is at room temperature and typically at a distance of only a few micrometers from the ultracold atoms, as sketched in Figure 1. Thermal current noise in the chip wires leads to magnetic near-field noise, potentially causing decoherence and trap loss at small atom-surface distance.

Figure 2: Hyperfine structure of 87Rb. We create superpositions of the states |0> and |1> to investigate their coherence lifetime.

In our experiment, we have investigated the coherence properties of atomic internal states superpositions on an atom chip. We create superpositions of the hyperfine ground state pair |0>=|F=1,mF=-1> and |1>=|F=2,mF=1> of ⁸⁷Rb shown in Figure 2. This state pair is both magnetically trappable and very robust against decoherence due to magnetic field noise, since both states have approximately equal magnetic moments. The states are coupled by a two-photon microwave+rf transition.

With a thermal ensemble of ultracold atoms close to quantum degeneracy, we perform Ramsey spectroscopy to determine the coherence lifetime. Figure 3 shows time-domain Ramsey fringes observed with atoms in a magnetic microtrap on the atom chip. The top layer of the chip used in these measurements is a 250 nm thick silver layer, which is the dominant source of magnetic near-field noise at micrometer distance.

Figure 3: Ramsey spectroscopy of the |0>-|1> transition with atoms held at a distance d = 9 micrometers from the chip surface. An exponentially damped sine fit to the Ramsey fringes yields a coherence lifetime of ~2.8 s. Each data point corresponds to a single shot of the experiment.

By performing such measurements at different atom-surface distances d, we have searched for a possible dependence of the coherence lifetime on d. With atoms at d = 5 - 130 micrometers from the chip surface, we observe coherence lifetimes exceeding 1 s. These lifetimes are independent of the atom-surface distance within our measurement accuracy and agree well with those observed in macroscopic magnetic traps.

Similar to the observations made by other groups, we do however observe a decrease in trap lifetime from 11 s at d > 20 micrometers to 1.6 s at d = 5 micrometers, caused by surface-induced evaporation and spin flips due to magnetic near-field noise. Our coherence measurements show that for the robust state pair |0> and |1>, there is no decrease in coherence beyond this decrease in trap lifetime.

Figure 4: Allan variance determined from frequency-domain Ramsey fringes with a time separation of T_R = 1 s between the pi/2-pulses.

The observation of trap and coherence lifetimes both exceeding 1 s at a few micrometers distance from the chip surface is an extremely encouraging result for atom chip applications.
We experimentally demonstrate the usefulness of our state pair in precision metrology. Because of the absence of surface-induced decoherence, a miniaturized atomic clock can be realized on the chip. Figure 4 shows a measurement of the Allan variance of the atomic clock in our experiment.
For this measurement, we set the two-photon drive to the slope of a Ramsey fringe and repeat the experiment many times. Any frequency drift of the atomic resonance relative to the quartz reference oscillator shows up as a drift in the measured atom number in state F=2. For integration times > 1000 s, the Allan variance is dominated by the drift of the quartz reference oscillator.

A detailed analysis of the noise sources in our experiment shows that the stability of our atomic clock is limited by ambient magnetic field fluctuations, fluctuating collisional shifts of the transition frequency caused by shot-to-shot fluctuations in atom number, and noise of the detection system. Straightforward improvements, such as magnetic shielding of the apparatus and atom-number normalized detection is expected to lead to a stability of ~10^-13/sqrt(Hz). While this does not reach the stability level of fountain clocks, a chip-based clock has the advantage of a simple, compact, and portable setup.

These experiments were published in P. Treutlein et al., Phys. Rev. Lett. 92, 203005 (2004), see our list of publications. An improved version of the atom chip atomic clock is currently being set up at SYRTE / Observatoire de Paris.