We convert a strongly interacting ultracold Bose gas into a mixture of atoms and molecules by sweeping the interactions from resonant to weak. By analyzing the decay dynamics of the molecular gas, we show that in addition to Feshbach dimers it contains Efimov trimers. Typically around 8% of the total atomic population is bound into trimers, identified by their density-independent lifetime of about 100 µs. The lifetime of the Feshbach dimers shows a density dependence due to inelastic atom-dimer collisions, in agreement with theoretical calculations. We also vary the density of the gas across a factor of 250 and investigate the corresponding atom loss rate at the interaction resonance.Experiments with ultracold atomic gases provide access to a vast array of intriguing phenomena, in part because of magnetically tunable Feshbach resonances. In particular, recent experimental [1][2][3][4][5] and theoretical [6][7][8][9][10][11][12][13][14][15][16] advances have made resonantly interacting Bose gases an exciting new research topic [17]. Unlike their fermionic counterparts, strongly interacting Bose systems are profoundly influenced by three-body phenomena, and help us understand the progression from two-through few-to many-body physics.At the Feshbach resonance the s-wave scattering length a diverges, and in the case of zero density the Feshbach molecule state, also of size a, merges with the free-atom state. This diatomic resonant scenario is the prelude for a set of exotic few-body phenomena, namely the Efimov effect. Although the Feshbach molecular state is unbound at the resonance, there exists an infinite log-periodic series of Efimov three-body bound states [18,19]. At 1/a → 0 the size of the p th Efimov state (p = 0, 1, 2...) is larger than the previous by a factor by 22.7, and its binding energy ET smaller by a factor of 22.7 2 [20,21]. At finite density n many-body effects complicate the physics. The system has an additional length scale, the interparticle spacing n −1/3 , that may determine how few-and many-body interactions scale. Many questions arise, such as: what are the structure, strength, length scale and dynamics of the two-, few-and many-body correlations? What does it mean to have a two-or three-atom molecule when it is embedded in a gas with interparticle spacing comparable to the molecular size?Both the ambiguous constitution of two-and three-body states in a many-body environment and the short-lived quasiequilibrium of a resonantly interacting Bose gas [3] complicate experiments. For these reasons, many experiments simplify matters by reducing interactions to a well-understood regime before imaging [1][2][3][4]. This interaction sweep can preserve resonance fossils in the form of perceived loss [1, 2, 4], momentum generation [3], and molecule formation.In this letter, we create a mixture of 85 Rb (free atoms), 85 Rb * 2 (Feshbach dimers), and 85 Rb * 3 (Efimov trimers) by sweeping a resonantly interacting degenerate Bose gas onto the molecular states in the weakly-interacting regime (na 3 1). O...

We perform precise studies of two-and three-body interactions near an intermediate-strength Feshbach resonance in 39 K at 33.5820(14) G. Precise measurement of dimer binding energies, spanning three orders of magnitude, enables the construction of a complete two-body coupled-channel model for determination of the scattering lengths with an unprecedented low uncertainty. Utilizing an accurate scattering length map, we measure the precise location of the Efimov ground state to test van der Waals universality. Precise control of the sample's temperature and density ensures that systematic effects on the Efimov trimer state are well understood. We measure the ground Efimov resonance location to be at −14.08(17) times the van der Waals length r vdW , significantly deviating from the value −9.7 r vdW predicted by van der Waals universality. We find that a refined multi-channel three-body model, built on our measurement of two-body physics, can account for this difference and even successfully predict the Efimov inelasticity parameter η.

We demonstrate that a single sub-cycle optical pulse can be generated when a pulse with a few optical cycles penetrates through resonant two-level dense media with a subwavelength structure. The single-cycle gap soliton phenomenon in the full Maxwell-Bloch equations without the frame of slowly varying envelope and rotating wave approximations is observed. Our study shows that the subwavelength structure can be used to suppress the frequency shift caused by intrapulse four-wave mixing in continuous media and supports the formation of single-cycle gap solitons even in the case when the structure period breaks the Bragg condition. This suggests a way toward shortening high-intensity laser fields to few-and even single-cycle pulse durations.PACS numbers: 42.65. Re, 42.65.Tg, 42.50.Gy The recent development of ultrafast science technology allowed the generation of light pulses with durations down to few optical cycles. There is an increasing number of investigations and experiments which involve such ultrashort pulses in femtosecond and attosecond domains [1]. Applications also include control of chemical reactions in physicochemical processes [2], femtochemistry [3], biological multiphoton imaging [4] and coherent control schemes [5]. In order to study light-matter interaction under extreme conditions as the pulse approaches the duration of a single optical cycle, great efforts for the generation of still shorter pulses have been made [6][7][8]. In particular, for continuous media the concept of single-cycle nonlinear optics [9] as well as the notion of extreme nonlinear optics [10] were introduced. For these processes, the traditional frame of the slowly varying envelope approximation (SVEA) and the rotating wave approximation (RWA) is invalid [11].In the last decade, there has been a rapid progress in the field of materials with periodic structures, such as Bragg grating, photonic band gap crystals and waveguide arrays [12]. Such systems exhibit qualitatively novel and fascinating linear-optical, nonlinear-optical and quantum-optical properties which provides an attractive way to control the light propagation and lightmatter interaction. Nonlinear pulse propagation in periodic structures is of both fundamental and applied interest, particularly, as a potential basis for nonlinear filtering, switching and distributed-feedback amplification [13]. Few-cycle pulse propagation in continuous media can yield solitons. Solitons can also exist in periodic structures which is usually referred to as gap soliton since they only exist within the forbidden gap [14,15]. The gap soliton was primarily found in periodic Kerr-nonlinear media. An essentially different mechanism of gap soliton generation with self-induced transparency has been revealed in Bragg grating which consists of a periodic array of thin layers of a resonant two-level medium separated by half-wavelength nonabsorbing dielectric layers [16,17]. It should be pointed out that for such a structure, the thickness of each two-level medium layer is much smaller than...

No abstract

We theoretically investigate the effects of the excitation frequency on the plateau of high-order terahertz sideband generation (HSG) in semiconductors driven by intense terahertz (THz) fields. We find that the plateau of the sideband spectrum strongly depends on the detuning between the near-infrared laser field and the band gap. We use the quantum trajectory theory (three-step model) to understand the HSG. In the three-step model, an electron-hole pair is first excited by a weak laser, then driven by the strong THz field, and finally recombined to emit a photon with energy gain. When the laser is tuned below the band gap (negative detuning), the electron-hole generation is a virtual process that requires quantum tunneling to occur. When the energy gained by the electron-hole pair from the THz field is less than 3.17 times the ponderomotive energy (U p ), the electron and the hole can be driven to the same position and recombined without quantum tunneling, so that the HSG will have large probability amplitude. This leads to a plateau feature of the HSG spectrum with a high-frequency cutoff at about 3.17U p above the band gap. Such a plateau feature is similar to the case of high-order harmonics generation in 4