Erratum: Comparison of Spectral Linewidths for Quantum Degenerate Bosons and Fermions [Phys. Rev. Lett. 117, 213001 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.213001.

Comparison of Spectral Linewidths for Quantum Degenerate Bosons and Fermions.

We observe a dramatic difference in optical line shapes of a ^{4}He Bose-Einstein condensate and a ^{3}He degenerate Fermi gas by measuring the 1557-nm 2 ^{3}S-2 ^{1}S magnetic dipole transition (8 Hz natural linewidth) in an optical dipole trap. The 15 kHz FWHM condensate line shape is only broadened by mean field interactions, whereas the degenerate Fermi gas line shape is broadened to 75 kHz FWHM due to the effect of Pauli exclusion on the spatial and momentum distributions. The asymmetric optical line shapes are observed in excellent agreement with line shape models for the quantum degenerate gases. For ^{4}He a triplet-singlet s-wave scattering length a=+50(10)_{stat}(43)_{syst}a_{0} is extracted. The high spectral resolution reveals a doublet in the absorption spectrum of the BEC, and this effect is understood by the presence of a weak optical lattice in which a degeneracy of the lattice recoil and the spectroscopy photon recoil leads to Bragg-like scattering.

High-precision spectroscopy of the forbidden 2 3s1→2 1p1 transition in quantum degenerate metastable helium.

We have measured the forbidden 2 (3)S(1)→2 (1)P(1) transition at 887 nm in a quantum degenerate gas of metastable (4)He atoms confined in an optical dipole trap. The determined transition frequency is 338 133 594.4 (0.5) MHz, from which we obtain an ionization energy of the 2 (1)P(1) state of 814 709 148.6 (0.5) MHz. This ionization energy is in disagreement by >3σ with the most accurate quantum electrodynamics calculations available. Our measurements also provide a new determination of the lifetime of the 2 (1)P(1) state of 0.551 (0.004)(stat) ((-0.000)(+0.013))(syst) ns, which is the most accurate determination to date and in excellent agreement with theory.

Frequency metrology in quantum degenerate helium: direct measurement of the 2 3S1 --> 2 1S0 transition.

Precision spectroscopy of simple atomic systems has refined our understanding of the fundamental laws of quantum physics. In particular, helium spectroscopy has played a crucial role in describing two-electron interactions, determining the fine-structure constant and extracting the size of the helium nucleus. Here we present a measurement of the doubly forbidden 1557-nanometer transition connecting the two metastable states of helium (the lowest energy triplet state 2 (3)S(1) and first excited singlet state 2 (1)S(0)), for which quantum electrodynamic and nuclear size effects are very strong. This transition is weaker by 14 orders of magnitude than the most predominantly measured transition in helium. Ultracold, submicrokelvin, fermionic (3)He and bosonic (4)He atoms are used to obtain a precision of 8 × 10(-12), providing a stringent test of two-electron quantum electrodynamic theory and of nuclear few-body theory.

Comparison of the Hanbury Brown-Twiss effect for bosons and fermions.

Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source, highlighting the importance of two-photon correlations and stimulating the development of modern quantum optics. The quantum interpretation of bunching relies on the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterization of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect (a tendency to avoid each other). Antibunching of fermions is associated with destructive two-particle interference, and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: (3)He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom-atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.

Degenerate Bose-Fermi mixture of metastable atoms.

We report the observation of simultaneous quantum degeneracy in a dilute gaseous Bose-Fermi mixture of metastable atoms. Sympathetic cooling of helium-3 (fermion) by helium-4 (boson), both in the lowest triplet state, allows us to produce ensembles containing more than 10(6) atoms of each isotope at temperatures below 1 microK, and achieve a fermionic degeneracy parameter of T/TF = 0.45. Because of their high internal energy, the detection of individual metastable atoms with subnanosecond time resolution is possible, permitting the study of bosonic and fermionic quantum gases with unprecedented precision. This may lead to metastable helium becoming the mainstay of quantum atom optics.

Simultaneous magneto-optical trapping of a boson-fermion mixture of metastable helium atoms.

We simultaneously confine fermionic metastable 3He atoms and bosonic metastable 4He atoms in a magneto-optical trap. The trapped clouds, containing up to 1.5 x 10(8) atoms of each isotope, are characterized by measuring ions and metastable helium atoms escaping from the trap. Optical pumping of 3He atoms to a nontrapped hyperfine state is investigated and it is shown that large atom numbers can be confined without additional repumping lasers. Unique possibilities for quantum degeneracy experiments with mixtures of spin-polarized metastable 3He and 4He atoms are indicated.

Photoassociation spectroscopy of cold He(2 3S) atoms

We observe vibrational states by photoassociation spectroscopy of cold He(2 3S) atoms. Photoassociation resonances are detected as peaks in the Penning ionization rate over a frequency range of 20 GHz below the atomic 2 3S1-2 3P2 transition frequency. We have observed three vibrational series, of which two can be identified. A possible mechanism to explain the observed increase of the Penning ionization rate is discussed.

Photoassociation spectroscopy of cold he(2

We observe vibrational states by photoassociation spectroscopy of cold He(2 ^{3}S) atoms. Photoassociation resonances are detected as peaks in the Penning ionization rate over a frequency range of 20 GHz below the atomic 2 ^{3}S_{1}-2 ^{3}P_{2} transition frequency. We have observed three vibrational series, of which two can be identified. A possible mechanism to explain the observed increase of the Penning ionization rate is discussed.

Laboratory measurements and T-matrix calculations of the scattering matrix of rutile particles in water.

We present experimentally determined scattering matrix elements of birefringent rutile particles in water as a function of the scattering angle for a wavelength of 633 nm (in air). These elements are compared with the results of T-matrix calculations for prolate spheroids. For the diagonal matrix elements the results of the T-matrix calculations are in good agreement with those of the measurements. A good fit for the whole matrix, including the off-diagonal elements, is obtained when we compensate for the birefringence of the rutile particles by performing the computations for spheroids with a slightly larger length/width ratio than measured.