Pancharatnam's phase advance and its validity for both integral and half-integral spins

Estevan Nunez

In 1950, Ramsey and Hahn separately described a method using separated oscillatory magnetic fields and electronic levels to measure interference in atomic states. Today, similar physics is exploited to make atom interferometer sensors utilizing what is called the spin-echo sequence. In 1956, Pancharatnam described the geometric phase difference between two polarized states of light. In 1984 Berry described the phase accrued in cyclic and adiabatic quantum systems. A Pancharatnam-Berry phase experiment involving a quarter-wave – half-wave – quarter-wave plate stack of optics and an experiment using the spin-echo sequence are based on seemingly different phenomena in optics versus atomic optics, respectively. However, the mathematical representations used to describe the Pancharatnam-Berry phase in optics are identical to those used to describe the spin-echo sequence. Therefore, the relationship between the spin-echo sequence and the Pancharatnam-Berry phase was explored. Experiments to test the comparisons using a pre-existing cold atom experiment, ~150 μK, were performed. The mathematical connection between the two types of experiments was explained more deeply.

Reyad Salah, Marwa M. Anwer, Mahmoud Abdel‐Aty

Kaiyuan Cao, Shuxiang Yang, Yayun Hu +1 more

The dynamics of the geometric phase are studied in inhomogeneous quantum spin chains after a quench. Analytic expressions of the Pancharatnam geometric phase (PGP) are derived for both the period-2 quantum Ising chain (QIC) and the disordered QIC. In the period-2 QIC, due to the periodic modulation, the phase difference between the boundaries of the half Brillouin zone $(0,\ensuremath{\pi}]$ changes with time, and consequently, the winding number ${\ensuremath{\nu}}_{D}(t)$ of the PGP is not quantized and thus is not topological anymore. Nevertheless, the PGP and its winding number show nonanalytic singularities at the critical times of the dynamical quantum phase transitions (DQPTs). This relation between the PGP and the DQPT is further confirmed in the disordered QIC. It is found that the critical time of the DQPT inherited from the homogeneous system and the additional one induced by weak disorder are also accompanied by the nonanalytic singularity of the PGP by decomposing the PGP into each quasiparticle mode. The connection between the nonanalytic behavior of the PGP at the critical time and the DQPT, regardless of whether the winding number is topological, can be explained by the fact that they both arise when the Loschmidt amplitude vanishes.

L. S. F. Olavo, Anníbal Dias Figueiredo

Long Chen, Jian Wei You, Ze Gu +2 more

Abstract The emergence of information metamaterials has spurred significant advances in the field of information sciences. However, the current studies are predominantly focused on classical bits as the fundamental information units, and the classical bit can only be located at two poles of Bloch sphere, resulting in limited information capacity. To break such limit, quantum bits (qubits) offer a promising solution since they have superposition states anywhere on the Bloch sphere. Here, a Pancharatnam‐Berry (PB) phase metasurface is used to emulate the qubits. Firstly, it proposes a theoretical concept of analog quantum bit and develops its mathematical and geometrical representations. Subsequently, a meta‐atom is designed as a physical platform to implement the concept of analog qubits. By manipulating the geometric configuration of the proposed meta‐atom, it achieves arbitrary superpositions of polarization states. A PB phase metasurface is experimentally fabricated to validate that the proposed analog qubit can be used to emulate the quantum bit in terms of both mathematical and geometrical representations. This work not only provides a theoretical foundation to go beyond the information limit of classical bits but also develops a feasible physics platform to investigate quantum information metasurfaces, which would complement and revolutionize classical information science.