Optically controlled spin-glasses generated using multi-qubit cavity systems

Recent advances in nanofabrication and optical control imply that multi-qubit-cavity systems can now be engineered with pre-designed couplings. Here we propose optical realizations of spin-glass systems which exploit these new nanoscale technologies. By contrast with traditional realizations using magnetic solids, phase transition phenomena can now arise in both the matter and radiation subsystems. Moreover the phase transitions are tunable simply by varying the matterradiation coupling strength. [email protected] [email protected] 1 Condensed matter physicists are keen to identify candidate materials in which one could examine the predicted theoretical properties of Ising-like Hamiltonians, both in the presence and absence of disorder [1]. Exotic phases such as a spin-glass are of particular interest [2, 3]. Most studies to date have focused on solids containing arrays of magnetic ions [1]. However the laws of Nature limit the diversity exhibited by such solids: It is very hard to engineer the magnitude, anisotropy, range and/or disorder of the spin-spin interaction in such systems. It is also hard to engineer the associated on-site energy for single spinflips. Hence it is highly desirable to identify new systems where one could engineer the on-site energies and spin-spin interactions at will. In the seemingly unrelated fields of atomic physics, nanostructure materials science and quantum optics, there have been remarkable advances in the fabrication and manipulation of matter-radiation systems [4]. The energy gaps in semiconductor quantum dots [5] can be engineered by varying the dot size and choice of materials. For example, vanishingly small optical gaps could be obtained using InAs/GaSb or HgTe/CdTe quantum dots, while vanishingly small inter-subband gaps can be obtained by increasing the dot’s size [5]. Hence tailormade two-level ‘qubit’ (i.e. quantum bit) systems are possible [6]. Indeed quantum dots are currently being fabricated and studied experimentally with sizes in the range 102−103 Angstroms, with various shapes, and from a range of III-V and II-VI semiconductors [5]. Experimental control of qubit-cavity couplings has already been demonstrated [7] for quantum dots coupled to photonic band-gap defect modes [8], as well as for atomic and superconducting qubit systems. A qubit-qubit interaction arises from the electrostatic inter-dot dipoledipole interaction between excitons (if the two-level system involves the optical gap) or conduction electrons (if the two-level system involves two adjacent conduction subbands). This qubit-qubit interaction can be engineered by adjusting the quantum dots’ size, shape, separation, orientation and the background electrostatic screening. The qubit-qubit interaction anisotropy can be engineered by choosing asymmetric dot shapes. Disorder in the qubit-qubit interactions can be introduced by choosing the individual dot positions during fabrication, but also arises naturally for self-assembled dots [5, 9]. All the pieces are therefore in place for engineering all-optical realizations of condensed matter spin-based systems. The problem is that we need to identify which multi-qubit-cavity system to build in order to mimic the particular spin-based Hamiltonian or phenomenon of interest. In this paper, we propose novel realizations of spin-glasses [2, 3] using experimentally feasible multi-qubit-cavity systems. By contrast with traditional realizations using magnetic solids, phase transition