The ability of quantum systems to exhibit interference between different quantum states is central to various fields of modern-day research, ranging from quantum simulator technology to the foundations of quantum theory. In the latter case, observing interference involving an increasingly large number of particles serves for testing the applicability limits of quantum mechanics. Quantum interference requires coherent quantum superpositions. However, quantum coherence is typically lost as a result of interactions between the system of interest and the environment.
We propose a method for protecting fragile quantum superpositions in many-particle systems from dephasing by external classical noise. We call superpositions “fragile” if dephasing occurs particularly fast, because the noise couples very differently to the superposed states. The method consists of letting a quantum superposition initially evolve under the internal dynamics of the system, then to reverse this dynamics at time t_0 by changing the sign of the interaction Hamiltonian, and, finally, to recover the initial superposition at time 2t_0. Such a procedure is used to generate the so-called “Loschmidt echo”, also known as “magic echo” in nuclear magnetic resonance. A Loschmidt-echo manipulation in the presence of internal interactions not only reverses internal decoherence but also suppresses dephasing due to external noise. The interaction Hamiltonian of the system must be chosen such that, for each of the superposed states, the expectation value of the variable coupled to the noise decays on the timescale much faster than t_0 and, as a result, the superposed states become much less distinguishable for the noise during most of the time interval [0,2t_0]. Therefore, the thermalization dynamics makes the superposed states almost indistinguishable during most of the above procedure.
We validate the method by applying it to a cluster of spins-½. By means of direct numerical integration of the Schroedinger equation, we calculate the lifetime of coherent superpositions for two cases: with and without applying the above method. In the concrete examples considered, the lifetime of coherent superpositions was shown to increase by two orders of magnitude.
