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arXiv:1912.05952 · Physical review. B./Physical review. B

Decoherence of a singlet-triplet superposition state under dipolar interactions of an uncorrelated environment

Patrick Vorndamme, Jürgen Schnack

Published Feb 3, 2020• 8 citations
arXivHTMLPDF

Abstract

Recently, it was shown that by means of an scanning tunneling microscope it is experimentally possible to stimulate clock transitions between the singlet and the nonmagnetic triplet state of a Heisenberg-coupled spin dimer [Bae et al., Sci. Adv. 4, eaau4159 (2018)]. This leads to more strongly protected clock transitions while ordinary ones only provide first-order protection against magnetic noise. However, large decoherence times of clocklike states normally refer to ensembles of spins which do not dephase. In the cited experiment, only one single dimer is manipulated and not an ensemble. For this reason, we simulate how a single dimer behaves in an environment of other spins which couple to the dimer via dipolar interactions. We perform unitary time evolutions in the complete Hilbert space, including dimer and a reasonably large environment. We will see that for a weak environment, this approach confirms long decoherence times for the clocklike state, but with stronger couplings this statement does not hold. As a reference, we compare the behavior of the dimer with other, non-clock-like, superposition states. Furthermore, we show that the internal dynamics of the bath plays an important role for the decoherence time of the system. In a regime where the system is weakly coupled to the bath, stronger interactions among environmental spins worsen the decoherence time up to a certain degree, while if system and bath are strongly coupled, stronger interactions in the environment improve decoherence times.

DOI
10.1103/physrevb.101.075101

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Recently, it was shown that by means of an scanning tunneling microscope it is experimentally possible to stimulate clock transitions between the singlet and the nonmagnetic triplet state of a Heisenberg-coupled spin dimer [Bae et al., Sci. Adv. 4, eaau4159 (2018)]. This leads to more strongly protected clock transitions while ordinary ones only provide first-order protection against magnetic noise. However, large decoherence times of clocklike states normally refer to ensembles of spins which do not dephase. In the cited experiment, only one single dimer is manipulated and not an ensemble. For this reason, we simulate how a single dimer behaves in an environment of other spins which couple to the dimer via dipolar interactions. We perform unitary time evolutions in the complete Hilbert space, including dimer and a reasonably large environment. We will see that for a weak environment, this approach confirms long decoherence times for the clocklike state, but with stronger couplings this statement does not hold. As a reference, we compare the behavior of the dimer with other, non-clock-like, superposition states. Furthermore, we show that the internal dynamics of the bath plays an important role for the decoherence time of the system. In a regime where the system is weakly coupled to the bath, stronger interactions among environmental spins worsen the decoherence time up to a certain degree, while if system and bath are strongly coupled, stronger interactions in the environment improve decoherence times.
Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. These applications require protection of the spin states against quantum decoherence due to interactions with the environment. While a single spin is easily disrupted, a coupled-spin system can resist decoherence by using a subspace of states that is immune to magnetic field fluctuations. Here, we engineered the magnetic interactions between the electron spins of two spin-1/2 atoms to create a "clock transition" and thus enhance their spin coherence. To construct and electrically access the desired spin structures, we use atom manipulation combined with electron spin resonance (ESR) in a scanning tunneling microscope. We show that a two-level system composed of a singlet state and a triplet state is insensitive to local and global magnetic field noise, resulting in much longer spin coherence times compared with individual atoms. Moreover, the spin decoherence resulting from the interaction with tunneling electrons is markedly reduced by a homodyne readout of ESR. These results demonstrate that atomically precise spin structures can be designed and assembled to yield enhanced quantum coherence.
Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. These applications require protection of the spin states against quantum decoherence due to interactions with the environment. While a single spin is easily disrupted, a coupled-spin system can resist decoherence by using a subspace of states that is immune to magnetic field fluctuations. Here, we engineered the magnetic interactions between the electron spins of two spin-1/2 atoms to create a “clock transition” and thus enhance their spin coherence. To construct and electrically access the desired spin structures, we use atom manipulation combined with electron spin resonance (ESR) in a scanning tunneling microscope. We show that a two-level system composed of a singlet state and a triplet state is insensitive to local and global magnetic field noise, resulting in much longer spin coherence times compared with individual atoms. Moreover, the spin decoherence resulting from the interaction with tunneling electrons is markedly reduced by a homodyne readout of ESR. These results demonstrate that atomically precise spin structures can be designed and assembled to yield enhanced quantum coherence.
The decoherence of quantum objects is a critical issue in quantum science and technology. It is generally believed that stronger noise causes faster decoherence. Strikingly, recent theoretical work suggests that under certain conditions, the opposite is true for spins in quantum baths. Here we report an experimental observation of an anomalous decoherence effect for the electron spin-1 of a nitrogen-vacancy centre in high-purity diamond at room temperature. We demonstrate that, under dynamical decoupling, the double-transition can have longer coherence time than the single-transition even though the former couples to the nuclear spin bath as twice strongly as the latter does. The excellent agreement between the experimental and theoretical results confirms the controllability of the weakly coupled nuclear spins in the bath, which is useful in quantum information processing and quantum metrology. Quantum objects are subject to decoherence effects due to the surrounding environment. This study demonstrates experimentally a counterintuitive example of anomalous decoherence, in which electron spins residing at nitrogen vacancy centres in diamond display longer coherence times under stronger noises.
Decoherence of quantum objects in noisy environments is important in quantum sciences and technologies. It is generally believed that different processes coupled to the same noise source have similar decoherence behaviors and stronger noises cause faster decoherence. Here we show that in a quantum bath, the case can be the opposite. We predict that the multitransition of a nitrogen-vacancy center spin-1 in diamond can have longer coherence time than the single transitions, even though the former suffers twice stronger noises from the nuclear spin bath than the latter. This anomalous decoherence effect is due to manipulation of the bath evolution via flips of the center spin.
Single molecule magnets are novel mesoscopic materials exhibiting both classical and quantum properties. Revealing the decoherence and entanglement mechanisms in these systems is crucial for the applications in quantum information technologies. In this thesis, quantum tunneling of magnetization is studied in single molecule magnet dimer [Mn4]2. Motivated by the recent experiments demanding the modification of the current theories, phonon mediated spin bath decoherence model is proposed. In the first part of the thesis, the magnetization of the [Mn4]2 dimer under external magnetic field is investigated. Alternative entangled spin states involved in quantum tunnelings are identified by means of the exact solution of the Schrödinger equation and the Landau-Zener-Stückelberg method. Later, a decoherence model is introduced in which the interaction between the single molecule magnet (central spin) and spin bath is mediated by phonons in a coherent state or thermal distribution. It is observed that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times for coherent states and low temperature thermal distribution. In the former case, if the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important role in decoherence with increasing temperature. Possible effects of the temperature on spin bath contribution to decoherence is discussed. Then, the effect of entangled environment on decoherence is analyzed. Entanglement within environment is shown to reduce the decoherence of central spin. Also, the entanglement dynamics of the central bipartite spin system is studied. Classification of the Bell states is examined for common spin bath, and separate spin baths. Last part of the thesis is the analysis of dephasing in entangled qutrits (three level quantum systems) under the classical noise, and quantum decoherence. Density matrix formalism is shown to give equivalent results for both cases. For common and separate baths, robust and fragile Bell-like qutrit states were determined, and Horodecki's bound entangled state is shown to be more robust to decoherence in the latter case.
The clock transitions (CTs) or optimal working points (OWPs) of central qubits have long coherence times because their frequency fluctuations vanish in the linear order of external field noise (such as Overhauser fields from nuclear spin baths). Therefore, CTs (or OWPs) are useful for quantum technologies. Also, the quadratic dependence of frequencies on noises makes the CT decoherence an interesting physics problem. Thus we are motivated to study the decoherence of CTs. We consider noise from spin baths, which is one of the most relevant mechanisms of qubit decoherence. Various quantum many-body methods have been developed to study the decoherence of a central spin in spin baths. In particular, the cluster-correlation expansion (CCE) systematically accounts for the many-body correlations that cause the central spin decoherence. However, the CCE cannot be straightforwardly applied to CTs in spin baths, for the expansion may fail to converge due to the effective long-range interactions resulting from the quadratic term of the noise (e.g., the second-order interaction mediated by hyperfine interactions for a nuclear spin bath). In this work, we develop a modified CCE method to tackle this class of decoherence problems. By diagonalizing the central spin Hamiltonian for each bath eigenstate of the hyperfine interaction, we find that the effects of long-range interactions are absorbed as fluctuations of central spin eigenenergies in the form of single-spin correlations. We apply the method to two important systems, namely, nitrogen vacancy center electron spins in near zero magnetic field and the singlet-triplet transition of two electrons in a double quantum dot. The numerical simulation shows that the modified CCE converges rapidly for the CTs. This modified cluster correlation expansion provides a nonperturbative approach to treating the central spin mediated long-range interactions in central spin decoherence problems.