Experimental Demonstration of Direct Path State Characterization by Strongly Measuring Weak Values in a Matter-Wave Interferometer

Abstract

A novel method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently Vallone and Dequal showed theoretically that weak measurements are not a necessary condition to determine the weak value [Phys. Rev. Lett. 116, 040502 (2016)]. Here we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system's quantum state was characterized via direct measurements using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones. Our results are not limited to neutron interferometry, but can be used in a wide range of quantum systems. [17,18]. One can also take a pragmatic approach and simply treat the weak value as a complex number that is accessible by experiment, as done in direct state characterization [19,20] to determine complex quantum state probability amplitudes in a particular basis. The weak value of observable of a quantum system is given bywhere |ψ i and |ψ f are the initial (preselected) and final (postselected) system states respectively. To determine  w a probe system, which serves as a measurement apparatus, has to be coupled to the observed system, leading to an entanglement between them. In the usual weak measurement approach only minimally disturbing interactions, between the quantum system and the measurement apparatus are regarded. However, as was recently pointed out theoretically [21,22], the weakness of the interaction is not a necessary condition to obtain the weak value. Furthermore it was shown that strong measurements give a better direct measurement of the quantum wave function using the weak value.

A framework for measuring weak values without weak interactions and its diagrammatic representation

“…When the measured observable corresponds to the projection operator = A 2 or Pauli operator ŝ i (i=x, y, z), the strength of the system-probe interaction can be arbitrarily high [26][27][28][29]. In the former case [26,27,29], the interaction with the optimal coupling strength ξ=π/2, which maximally entangles the total state, can be described as , where P (1) is the probability that the initial state undergoes the transformationT , the system is projected onto y ñ | f , and the probe is projected onto ñ |1 .…”

“…In the former case [26,27,29], the interaction with the optimal coupling strength ξ=π/2, which maximally entangles the total state, can be described as , where P (1) is the probability that the initial state undergoes the transformationT , the system is projected onto y ñ | f , and the probe is projected onto ñ |1 . In the latter case [28], the interaction with the optimal coupling strength ξ=π/ in our framework, and the resulting complex value is y y s á ñ á ñ | | |ˆi f i 2 w , which includes the weak value s á ñ i w . When the measured observable is arbitrary and the strength of the system-probe interaction ξ is arbitrarily high, a modular value is used as the parameter of a pre-and post-selected quantum systems (instead of the weak value) that provides a complete description of its effect on the qubit probe [30].…”

“…However, this is not the only possible method for their determination, and several alternative weak value measurement techniques that do not involve weak system-probe interactions have been recently developed, including those using strong system-probe interactions [26][27][28][29], modular values [30], quantum control interactions [31,32], an enlarged Hilbert space [33], coupling-deformed pointer observables [34], and a combination of several strong measurements of the system [35]. It should be noted here that most of them [26][27][28][29][30][31][32][33] and some weak measurement experiments [2][3][4][5][6][7][8][9][10][16][17][18][19][20][21][22][23][24] use qubit systems as the probes. They all have the same measurement procedure of the qubit probes to obtain complex weak values-measuring expectation values of two operators, such as Pauli-X and Pauli-Y.…”

Interaction-Free Effects Between Distant Atoms

“…For example, an analysis performed using the TSVF approach within quantum mechanics suggested that the born/unborn photon has unique physical properties [57,58]. Moreover, recent experiments [59,60] and thought experiments [61][62][63] employ strong rather than weak measurements for analyzing new phenomena. A subsequent work [18], based on Davies et al [57,58], examines through the analysis of weak values the evolution between two strong "no-emission" measure-ments: the wave-function is first weakly radiated and then weakly "drawn back" to its still-excited atom.…”

Confined contextuality in neutron interferometry: Observing the quantum pigeonhole effect

“…However, neither the BKS theorem, nor these experiments, specify which contexts are contradictory. In this article, using recently developed weak measurement techniques in neutron interferometry [14][15][16][17][18][19][20], we experimentally demonstrate which specific measurement context within a BKS-set (Fig. 1a) must contain contradictory value assignments, essentially confining the contextuality [21].…”