Adiabatic Mach-Zehnder interferometer via an array of trapped ions

Abstract

We explore the possibility of implementing a Heisenberg-limited Mach-Zehnder interferometry via an array of trapped ions, which obey a quantum Ising model within a transverse field. Based upon adiabatic processes of increasing the Ising interaction and then decreasing the transverse field, we demonstrate a perfect transition from paramagnetism to ferromagnetic states, which can be used as the beam splitter for the multi-ion Mach-Zehnder interferometry. The achieved NOON state of the ions enables the Heisenberg-limited interferometry. Using currently available techniques for ultracold ions, we discuss the experimental feasibility of our scheme with global operations.PACS numbers: 03.75. Dg, 03.67.Ac, 37.10.Ty Since the foundation of quantum theory, as a natural result of superposition principle, quantum interference has attracted continuous attentions in both theoretical and experimental studies. It has been widely used to implement high-precision measurement, quantum information processing and so on. A well-known scheme for performing quantum interferometry is the Mach-Zehnder (MZ) interferometry, which has a beam splitter for splitting the input states and another beam splitter for recombining the output states. Up to now, quantum MZ interferometry has been accomplished via photons Beyond the conventional quantum interferometry via unentangled states, it has been demonstrated that the measurement precision can be enhanced from the standard quantum limit (or the shot noise limit) to the Heisenberg limit by using multipartite entangled states [6]. An excellent candidate is the NOON state2, which is an equal-probability superposition of all N particles in one of two paths denoted by a and b. The entangled ions for highprecision metrology have been proposed theoretically [7] and demonstrated experimentally [8,9]. However, these schemes are subject to limited numbers of ions or the requirement for individual addressing. For an ensemble of thousands of neutral atoms, the possibility of performing a Heisenberg-limited MZ interferometry has been demonstrated via a quantized Bose-Josephson junction [10].In this article, based upon the adiabatic processes and global operations on an array of ultracold ions, we present a realizable scheme for performing a Heisenberg-limited MZ interferometry. The ion array is described by a quan- * Electronic address: huyanmin2003@163.com † Electronic address: mangfeng@wipm.ac.cn ‡ Electronic address: chleecn@gmail.com tum Ising model of ferromagnetic (FM) interaction J and transverse field B, which has been used to simulate quantum magnetism [11][12][13] and quantum phase transition (QPT) [14][15][16] by virtue of spin-dependent optical dipole forces [17]. In our scheme, if the system starts from a paramagnetic state dominated by B, we adiabatically increase J and then decrease B, and vice versa if the system starts from a FM state dominated by J. In contrast to tuning either J or B in previous schemes [11,16], the adiabatic processes in our scheme perfectly connects the two limits so...

Quantum simulation

“…This was among the first experimental realizations of quantum simulation. More recently, the study of Mach-Zehnder interferometry with an array of trapped ions was explored in (Hu et al, 2012).…”

“…Ions (Leibfried et al, 2002)*, (Hu et al, 2012;Lau and James, 2012) Photons (Aaronson and Arkhipov, 2011), (Broome et al, 2013)*, (Crespi et al, 2013;Spring et al, 2013;Tillmann et al, 2013)* Superconducting circuits (Liao et al, 2010;Zhou et al, 2008a) Other applications:…”

Quantum Metrology With Cold Atoms

“…Ultracold trapped ions have been proposed to explore fundamental quantum principle and implement quantum information processing, 85,[190][191][192][193][194][195][196][197] quantum simulation 198,199 and quantum metrology. 24,30,85,143,144,200 Here, we give a brief introduction for some typical experiments of quantum metrology via ultracold trapped ions. In 2001, Meyer et al experimentally demonstrated that the sensitivity of rotation angle estimation with a Ramsey spectroscopy can be improved by using entangled trapped ions.…”

“…A central goal of quantum metrology is how to enhance measurement precision with quantum resources such as spin squeezing and multiparticle entanglement. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] For a multiparticle system of cold atoms, it has been demonstrated that quantum entanglement and spin squeezing can be prepared by employing intrinsic inter-atom interactions or laser induced artificial inter-atom interactions. [27][28][29] Up to now, cold atoms have been widely used for implementing precision metrology, such as interferometers, [30][31][32] gyroscopes, 33 quantum clocks, [34][35][36] magnetic field detectors [37][38][39][40] and micro-gravity sensors.…”

Manipulating Schrödinger Cat State of an Ising Chain via Quantum Tunneling Effect

“…10,11 Although the Cat state with six ions in chain has been feasible experimentally, 12 the generation of a large-scale Cat state with more qubits is still a fascinating challenge both theoretically and experimentally. The trapped-ion system is a promising candidate in this respect 6,7,12,13 due to the capability of 14-qubit entanglement in Ref. 14.…”