Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. So far, these "contact" relations have been established only for interactions with s-wave symmetry, i.e., without relative angular momentum.We report measurements of two new physical quantities, the "p-wave contacts", and present evidence that they encode the universal aspects of p-wave interactions through recently proposed relations. Our experiments use an ultracold Fermi gas of 40 K, in which s-wave interactions are suppressed by polarising the sample, while p-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new contact relations, we infer an attractive p-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant p-wave quantum gas. 1 arXiv:1505.08151v4 [cond-mat.quant-gas] 13 Apr 2016 A fundamental question provoked by observation of natural systems is how macroscopic and collective properties depend on microscopic few-body interactions. Ultracold neutral atoms provide a model system in which to explore this question, since in certain conditions,few-body interactions can be tuned and characterised precisely. Over the last decade, a direct link has been made in these systems between thermodynamic properties and the underlying isotropic (s-wave) interactions. At the centre stage is a quantity called the "contact" [1][2][3][4][5][6], which describes how the energy of a system changes when the interaction strength is changed. Surprisingly, the contact is also the pivot of a set of universal relations, that constrain numerous microscopic properties, including the two-particle correlation function at short range. These relations apply regardless of temperature, density, or interaction strength [1-3, 5], to fermions and bosons [7][8][9], and in one-, two-, and three-dimensional systems [7,[10][11][12]. Contact relations have also been extended to Coulomb gases [13] and neutron-proton interactions [14]. Despite the breadth of this discussion, measurements of the contact have so far been restricted to systems with s-wave interactions.In general, the relative wave function of any pair of particles can be decomposed into components with angular momentum equal to an integer multiple of quanta. In a spinpolarised Fermi gas, quantum statistics forbids short-range interactions with even values of . Therefore, the first allowed scattering channel has = 1 (p-wave), which is typically weak due to the centrifugal barrier (see Fig. 1): the scattering cross section decreases with the square of...
BackgroundColorectal cancer is the 4th common cancer in China. Most colorectal cancers are due to modifiable lifestyle factors, but few studies have provided a systematic evidence-based assessment of the burden of colorectal cancer incidence and mortality attributable to the known risk factors in China.MethodsWe estimated the population attributable faction (PAF) for each selected risk factor in China, based on the prevalence of exposure around 2000 and relative risks from cohort studies and meta-analyses.ResultsAmong 245,000 new cases and 139,000 deaths of colorectal cancer in China in 2012, we found that 115,578 incident cases and 63,102 deaths of colorectal cancer were attributable to smoking, alcohol drinking, overweight and obesity, physical inactivity and dietary factors. Low vegetable intake was the main risk factor for colorectal cancer with a PAF of 17.9%. Physical inactivity was responsible for 8.9% of colorectal cancer incidence and mortality. The remaining factors, including high red and processed meat intake, low fruit intake, alcohol drinking, overweight/obesity and smoking, accounted for 8.6%, 6.4%, 5.4%, 5.3% and 4.9% of colorectal cancer, respectively. Overall, 45.5% of colorectal cancer incidence and mortality were attributable to the joint effects of these seven risk factors.ConclusionsTobacco smoking, alcohol drinking, overweight or obesity, physical inactivity, low vegetable intake, low fruit intake, and high red and processed meat intake were responsible for nearly 46% of colorectal cancer incidence and mortality in China in 2012. Our findings could provide a basis for developing guidelines of colorectal cancer prevention and control in China.
This corrects the article DOI: 10.1103/PhysRevLett.115.135304.
Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that, near an interaction resonance, shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.PACS numbers: 03.75. Hh, 05.30.Jp, 67.40.Db, 67.40.Vs Interatomic interactions limit the accuracy of atomic clocks, causing density-dependent clock shifts in radio frequency (rf) transitions. Similarly, such shifts play an important role in probing correlations in atomic gases [1], where, e.g., rf spectroscopy has been used to detect the presence of molecules and provide evidence for pairing gaps [2,3,4]. Surprisingly, experimentally observed clock shifts become small when interactions are resonantly enhanced [3,5], a result we explain here, first by developing a general theory of the average clock shift and then showing that in the strongly interacting regime the shifts depend inversely on interatomic scattering lengths.Single component spin-polarized Fermi gases do not experience clock shifts, since the rf coupling preserves polarization, forbidding s-wave interactions [5]. In addition, in mixtures of interacting fermions in two states |1 and |2 , e.g., the lowest two hyperfine states of 6 Li, clock shifts are absent for transitions |1 → |2 , since the interaction energy is invariant under the rf field [1]. Interactions in two-state mixtures can be probed, rather, by driving transitions to an initially empty state, e.g., in 6 Li, from |2 to the next hyperfine state |3 .Rf transitions in atoms are usually described in terms of coherent evolution of a two-level system undergoing Rabi oscillations, represented by rotations of an equivalent pseudospin on the Bloch sphere. In the present problem, the rf field rotates an atom in state |2 into a coherent superposition, |2 → |β = cos θ|2 + e −iφ sin θ|3 . (The angles φ and θ depend on time, the rf pulse power, and its detuning from resonance.) To the extent that interatomic interactions only shift the energy levels, but do not broaden the lines, the Bloch sphere picture is valid. However, strong interactions lead to an incoherent and irreversible evolution, and in the long-time, weak pulse regime the probability to find the system in a particular final state is given rather by Fermi's Golden Rule.We base our discussion on linear response theory (in Ref. [5] fewer than 30% of the atoms are transferred by the rf pulse, with comparable numbers in Ref. [3]). We consider a spatially uniform Fermi gas with three internal states, and Hamiltonian H = H 0 + H s , whereis the hyperfine plus Zeeman energy of level |i , and N i is the total number of atoms in state |i . The system Hamiltonian is (h = 1 throughout),. (1) Here v ij (r − r ′ ) is the bare potential between two atoms in |i and |j (not a low-energy effective interaction).The (e...
In this letter we consider spinless Fermi gases placed inside a cavity and study the critical strength of pumping field for driving a superradiance transition. We emphasize that Fermi surface nesting effect strongly enhances the superradiance tendency. Around certain fillings, when the Fermi surface is nearly nested with a relevant nesting momentum, the susceptibility of the system toward a checkboard density-wave ordered state is strongly enhanced, because of which a much smaller (sometime even vanishingly small) critical pumping field strength can lead to superradiance. This leads to interesting reentrance behavior and topologically distinct structure in the phase diagram. Away from these fillings, the Pauli exclusion principle brings about the dominant effect for which the critical pumping strength is lowered in the low-density regime and increased in the high-density regime, in comparison to a Bose gas with same density. These results open the prospect of studying rich phenomena of degenerate Fermi gases in cavity.Recently, a series of experiments have studied weakly interacting degenerate Bose gas in a cavity [1,2], in which superradiance induced density-ordered superfluid phase [1] and softening of roton excitations in the vicinity of a superradiance phase transition have been observed [2]. Studying degenerate quantum gases inside a cavity offers new insights to many-body systems [3]. First, cavity field is a dynamical photon field rather than a classical laser configuration; cavity photon modes affect the many-body system as dynamical variables. For examples, cavity photons can mediate an effective long-range interactions between atoms [4,5]; a multi-mode cavity can introduce frustration to atoms that enhances quantum fluctuations [6]. Second, the inevitable decay of cavity photons makes the system interesting for studying non-equilibrium phenomena.So far, limited attention has been paid to degenerate Fermi gases inside cavities [7][8][9]. However, there is no fundamental difficulty in realizing such a system experimentally. In free space without cavity, superradiance has been proposed theoretically for fermions [10,11] and subsequently demonstrated experimentally [12]. To stimulate experimental efforts along this direction, it is therefore desirable to theoretically investigate interesting physics in this setup. In this work we shall start from the simplest case, i.e. spinless fermions, and show that nontrivial effects already exist.In contrast to bosons, due to the Pauli exclusion principle, a degenerate Fermi gas forms a Fermi sea, occupying a collect of single particle states of lowest energies. Moreover, the system exhibits a Fermi surface (FS) where "Fermi surface nesting" is the crucial feature responsible for many collective phenomena in fermonic systems, such as charge-density wave, spin-density wave [13], as well as some strongly correlated unconventional superconductivity [14]. FS nesting means when a sizable portion of the FS shifted by a certain momentum overlaps with the original one. If a F...
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