Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1=3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect. Collective states of matter have proved enormously important both because of the conceptual structures they reveal and the role they play in technological innovation. The fractional quantum Hall (FQH) liquid, which emerges as a result of interactions between electrons when the dimensionality is reduced to two and the Hilbert space is further restricted by application of an intense magnetic field [1], represents a cooperative behavior that does not subscribe to concepts such as Bose-Einstein condensation, diagonal or off-diagonal long range order, and Landau order parameter. It is the realization of a topological quantum state of matter, the understanding of which has influenced development in a wide variety of fields, such as topological insulators, cold atoms, graphene, generalized particle statistics, quantum cryptography, and more [2][3][4][5][6][7].Neutral excitations provide a window into the physics of the FQH liquid. Early theoretical treatments of the lowest neutral collective mode of the FQH state at ¼ 1=3 employed a single mode approximation [8], as well as exact diagonalization studies on small systems [9], and showed a minimum in the dispersion, which, following the terminology used in superfluid helium, is called a ''magnetoroton.'' Subsequently, the collective modes at this and other fractions were understood in terms of composite fermions (CFs), quasiparticles that result from a binding of electrons and an even number of quantized vortices [10]. Despite their complex collective character, CFs act as almost free particles insofar as the low energy behavior is concerned [1]. They experience an effective magnetic field and form their own Landau-like levels, which are called ''Ã levels.'' (The CF Ã levels reside within the lowest electronic Landau level.) The neutral excitations are described as inter-Ã-level exciton collective modes of CFs [11][12][13][14], in close analogy to the electronic collective modes of the integral Hall states.We report the excitation spectrum of the FQH fluid at ¼ 1=3 in an unexplored energy range. Our main finding is the existence of several well-defined collective modes at energies substantially exceeding those of the highest before reported spin-conserving (SC) and spin-flip (SF) modes [15][16][17]. Further, we provide compelling evidence, supported by a detailed comparison between theory and experiment, that these neutral modes represent a new family of excitations involving CF ...

Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor ν = 1 and at very low temperatures (∼ 40 mK). A small change in filling factor (δν ≈ ±0.01) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at ν = 1 is surprisingly fragile against increasing temperature, or against small changes in filling factor. PACS numbers:Electron-electron interactions in two dimensions dominate in many cases over the single particle physics leading to new collective ground states of the system. This is particularly true in GaAs due to the small value of the single particle Zeeman energy. The physics in the vicinity of filling factor ν = 1 is particularly rich. The system behaves as a half empty Landau band in which all the electrons have the same orbital quantum number and only the spin degree of freedom remains. At exactly ν = 1, the predicted ground state is an itinerant quantum Hall ferromagnet [1,2], while on either side of ν = 1 the system depolarizes more rapidly than predicted by the single particle picture, due to the formation of spin textures (Skyrmions or anti-Skyrmions) in the ground state [3,4,5,6,7,8]. The strong coupling between the nuclear and electronic spin systems, observed close to ν = 1 in specific heat capacity [9], and resistively detected nuclear magnetic resonance (NMR) measurements [10], strongly suggest the existence of gapless spin excitations of the electronic system. Such Goldstone modes are consistent with a breaking of the spin rotational symmetry due to the formation of a Skyrme crystal in the ground state [11].Electrical transport measurements, which have been extensively used to investigate the quantum Hall effect, are not an incisive probe of the physics of the ground state at exactly integer filling factor, since the Fermi energy lies deeply inside localized states. Optical techniques such as photoluminescence, absorption and inelastic light scattering have been widely applied [8,12,13,14,15,16]. Surprisingly, techniques which give a direct measure of the spin polarization, suggest that the system is not fully spin polarized at ν = 1 [8,13,16], despite the large exchange enhanced spin gap which remains open even in the absence of the single particle Zeeman energy [7].In this paper we report on optical absorption (transmission) measurements to directly probe the subtle physics of the n=0 Landau level (LL) via the spin polarization of the system. We find that full spin polarization does indeed occur, but only at exactly filling factor ν = 1 and at very low (40 mK) temperatures. This suggest that the quantum Hall ferromagnet at ν = 1 is surprisingly fragile, collapsing, with either a small change of filling factor or temperature, into a lower energy ground state with a large number of reversed spins.To measure the absorption spectrum of a single GaAs quantum well (QW) at low temperatures we have used a structure which for...

We present measurements of optical interband absorption in the fractional quantum Hall regime in a GaAs quantum well in the range 0 < ν ≤ 1. We investigate the mechanism of singlet trion absorption, and show that its circular dichroism can be used as a probe of the spin polarization of the ground state of the two-dimensional electron system (2DES). We find that at ν ≤ 1/3 the 2DES is fully spin-polarized. Increasing the filling factor results in a gradual depolarization, with a sharp minimum in the dichroism near ν = 2/3. We find that in the range 0.5 ≤ ν < 0.85 the 2DES remains partially polarized for the broad range of magnetic fields from 2.75 to 11 Tesla. This is consistent with the presence of a mixture of polarized and depolarized regions.The electron-electron Coulomb interaction plays an important role in determining the spin polarization (P) of a two-dimensional electron system (2DES) in a perpendicular magnetic field B. The effect of the interactions on the spin is most readily seen in in the filling factor range ν ≤ 1, where the level degeneracy exceeds the number of electrons. The exchange part of the Coulomb interactions favors a ferromagnetic state. However, a manybody wavefunction in which all electrons have the same spin is restricted by the Pauli principle and may not constitute in general an optimal spatial distribution that minimizes the total Coulomb energy. Inclusion of components of the opposite spin in the wavefunction opens a larger phase space for the electrons and may result in a lower Coulomb repulsion. Thus, the ground state of the 2DES in this regime is determined by the competition between the gain in Coulomb energy and the cost in Zeeman energy.Several methods have been used to determine the 2DES spin polarization in the fractional quantum Hall regime. The direct method is measuring the shift in the nuclear magnetic resonance (NMR) caused by the 2DES magnetization. Indeed, NMR measurements have yielded quantitative measurements of P throughout a broad range of filling factors [1,2]. Transport experiments have also been used and were successful in identifying transitions in the spin polarization, although are less effective in providing a quantitative value of P [3, 4].An alternative approach for measuring P is using optical spectroscopy: photoluminescence [5], reflectivity [6], and absorption spectroscopy [7]. In these techniques, the occupation of each spin levels are obtained from measurements of the circular dichroism of the interband transitions. In quantum wells (QW), however, establishing the relation between the optical oscillator strengths (OS) and P presents a major difficulty. As a result of the strong interaction between the photo-created valence hole and the electrons, the spectrum in QWs is dominated by resonance peaks, associated with the neutral exciton, and charged excitons (trions). A further complication is introduced by the fact that in a trion, the two electrons can form a singlet or triplet wavefunctions [8,9]. Hence, it is essential to take into account the nat...