Experimental Study of the Validity of Quantitative Conditions in the Quantum Adiabatic Theorem

In classical physics, adiabatic processes do not involvea transfer of heat between the system and environment. Inquantum mechanics, the adiabatic theorem states that asystem that is initially in an eigenstate of the Hamilton-ian will remain in this eigenstate if the changes of thisHamiltonian are sufficiently slow [1,2]. While this quan-tum adiabatic theorem (QAT) is a well-established fact, itappears to be difficult to formulate a consistent quantumadiabatic condition (QAC), which unambiguously stateswhen the theorem applies and is both necessary andsufficient.A QAT is critical for developments in many areas ofphysics. It provides the foundation and interpretation of theLandau-Zener transition [3], the Gell-Mann–Low theorem[4], and Berry’s phase [5]. Quantum adiabatic processesare also used for some quantum algorithms [6,7], theaffectivity of which are based on the validity of the QAT[8].Recently, however, doubts were cast over the consis-tency of the QAT and the sufficiency of the QAC. Marzlinand Sanders first suggested a possible inconsistency of theQAT [9]. Although there are some questionable points intheir deduction [10], their main point triggered an extendeddiscussion [11]. Then Tong