tum distribution observed in the nongaussian fits signals the onset of FD quantum degen- eracy, as evidenced by the good agreement between the data and the theory line present- ed in Fig. 5. In fact, the comparison with theory suggests that our lowest temperatures are actually closer to T/ T F = 0.4, consistent with our 20% systematic uncertainty in T/T F (primarily due to uncertainty in N)(30). We detected the emergence of quantum degeneracy in a trapped gas of Fermionic atoms and observed a barrier to the evapora- tive cooling process in a two-component Fermi gas below 0.5 T F . We observed a non- classical momentum distribution and found that the total energy of the gas is larger than the classical expectation. This excess energy is a manifestation of the Pauli exclusion prin- ciple that gives rise to an expanded momentum distribution at low T/T F by forcing the atoms to fill higher motional states of the harmonic trap- ping potential. Even as T approaches zero, an ideal Fermi gas still has 3 4 k B T F en- ergy per particle; indeed, at our lowest T/T F  0.5 we measured an energy that is only 2.2 times this T = 0 limit. Reaching this quantum regime in the dilute Fermi gas extends the field of quantum degenerate gases and sets the stage for further experi- mental probes of a Fermi sea of atoms. References and Notes 1. See, for example, E. P. Bashkin and A. E. Meyerovich, J. Phys. Colloq. France 41, C7-61 (1980). 2. S. Inouye et al., Nature 392, 151 (1998); Ph. Courteille, R. S. Freeland, D. J. Heinzen, F. A. van Abeelen, B. J. Verhaar, Phys. Rev. Lett. 81, 69 (1998); J. L. Roberts et al., ibid., p. 5109; V. Vuletic, A. J. Kerman, C. Chin, S. Chu, ibid. 82, 1406 (1999). 3. For recent reviews, see E. A. Cornell, J. R. Ensher, C. E. Wieman, online abstract available at http://xxx.lanl. gov/abs/cond-mat/9903109; W. Ketterle, D. S. Durfee, D. M. 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Sto ¨cker, Thermodynamics and Statistical Mechanics (Springer-Verlag, New York, 1995), pp. 359 –362. 27. The kinetic energy extracted from the time-of-flight absorption images equals half the total energy of the harmonically confined gas (from the equipartition theorem). 28. M. O.-Mewes et al., Phys. Rev. Lett. 77, 416 (1996); M. J. Holland, D. S. Jin, M. L. Chiofalo, J. Cooper, ibid. 78, 3801 (1997). 29. T is obtained from the widths of the outer gaussian,  x and  z , in fits of the form given in Eq. 1. Although the effects of the FD statistics are less severe on the outer edges of the momentum distribution, these fits become less accurate as T/T F decreases. We made a correction to T that is at most 7% based on the measured T/T F and the results of identical fits to calculated (semiclassical) momentum distributions for an ideal Fermi gas. 30. The number of atoms N is calibrated by a florescence measurement, which has an uncertainty of 50% because of intensity variations across the laser beams. The trap frequencies are determined to better than 5% from center-of-mass oscillations of the trapped gas. 31. Supported by the National Institute of Standards and Technology, the NSF, and the Office of Naval Re- search. We thank C. Wieman, E. Cornell, and the other members of the JILA BEC group for useful discussions. 19 July 1999; accepted 16 August 1999 A Capacitance Standard Based on Counting Electrons Mark W. Keller, 1 * Ali L. Eichenberger, 1 John M. Martinis, 1 Neil M. Zimmerman 2 A capacitance standard based directly on the definition of capacitance was built. Single-electron tunneling devices were used to place N electrons of charge e onto a cryogenic capacitor C, and the resulting voltage change V was mea- sured. Repeated measurements of C = Ne/V with this method have a relative standard deviation of 0.3  10 –6 . This standard offers a natural basis for capacitance analogous to the Josephson effect for voltage and the quantum Hall effect for resistance. In the past four decades, there has been an accelerating trend in metrology toward stan- dards based on fundamental quantum proper- ties of nature. Until 1960, all units in what is now the International System of Units (SI) were based on carefully constructed artifacts and classical physics (1). Quantum physics first entered the SI in 1960, when the defini- tion of the meter was based on the wave- length of radiation from a transition in the Kr atom. A voltage standard based on the Jo- sephson effect was first adopted in 1972 and refined in 1990, and a resistance standard based on the quantum Hall effect was adopt- ed in 1990 (2, 3). For capacitance, the best existing standards are known as “calculable capacitors” and rely on a special arrangement of several electrodes such that the capaci- tance per unit length is related to the permit- tivity of free space (a defined constant in the SI) (4 ). Realizing such a standard requires precise alignment of electrodes of order 1 m in length, one of which must be movable, and compensation of end effects in order to make a system of finite length behave like an infi- nite system over a limited range. With the development over the past decade of single- electron tunneling (SET) devices that can precisely manipulate and detect single elec- trons (5), it is now possible to create a capac- itance standard based on the quantization of electric charge (6 ). Such a standard, which we describe here, places capacitance metrol- ogy on a quantum basis and is a natural complement to the voltage and resistance standards adopted in 1990 (7 ). Our capacitance standard combines SET de- vices and a low-loss cryogenic capacitor. We explain the operation of the standard, demon- strate its repeatability and uncertainty, and con- sider the prospects for developing our prototype into a practical calibration system. This stan- 1 National Institute of Standards and Technology, Boulder, CO 80303, USA. 2 National Institute of Stan- dards and Technology, Gaithersburg, MD 20899, USA. *To whom correspondence should be addressed. E- mail: mark.keller@boulder.nist.gov R EPORTS 10 SEPTEMBER 1999 VOL 285 SCIENCE www.sciencemag.org 1706