### Controlling Quantum Particles By Looking At Them

**[Left to Right] M.S. Blok, C. Bonato, R. Hanson.**

**Authors: M.S. Blok**

^{1}, C. Bonato^{1}, M.L. Markham^{2}, D.J. Twitchen^{2}, V.V. Dobrovitski^{3}, R. Hanson^{1}

**Affiliation:**

^{1}Kavli Institute of Nanoscience Delft, Delft University of Technology, The Netherlands.

^{2}Element Six Ltd, Ascot, Berkshire, UK.

^{3}Ames Laboratory and Iowa State University, Ames, Iowa, USA.Quantum measurements differ from their classical counterparts in the sense that they not only extract information from a system but also alter its state. The disturbance of a measurement, known as the measurement back-action, is probabilistic but can be used as a control tool when it is combined with real-time feedback. Here we show that we can manipulate a nuclear spin using only the back-action of sequential quantum measurements in combination with a feedback loop [1].

To gain control over the measurement back-action we exploited the fundamental trade-off between information gain and disturbance that is characteristic for quantum measurements [2-4]. Where a ‘conventional’ projective measurement gives maximal information, it also induces maximal disturbance since it collapses the system to an eigenstate, thus limiting the amount of accessible states. By using an intermediate particle as a probe to measure the system, one can create a tuneable amount of correlation between the system and the probe by letting them interact for a certain time (Fig 1a). A subsequent measurement of the probe will give no information about the system if the two were not correlated at all, meaning that the measurement back-action will be zero. When the two-system and the probe are maximally correlated, a projective measurement is performed. Thus by choosing a certain interaction time, one can tune the measurement strength and therefore control the amount of back-action associated with a measurement.

**Figure 1: a) Representation of a quantum measurement where a system (spin, pointing up or down) is coupled to a probe, in this case a quantum clock where the pointer either rotates clockwise or anticlockwise depending on the state of the system. b) Nitrogen-Vacancy center in diamond and the two spins associated with it.**

We demonstrated these variable strength measurements using an NV-center in diamond. This is a defect in the diamond lattice consisting of a Nitrogen atom and a vacancy at an adjacent lattice position (Fig 1b). As a system we used the spin of the nitrogen atom, while the probe is implemented by the electron spin associated with the NV-center. At low temperatures (4K) the electron spin can be readout in a single shot using spin-selective optical transitions [5] and manipulated using MW pulses. The interaction is governed by the hyperfine coupling and it can effectively be turned on by bringing the electron in a superposition. In figure 2 a we show that we can tune the amount of information by plotting the probe (electron) readout for varying interaction time in a Ramsey-type experiment. In Figure 2 b we show the state of the system after a variable strength measurement, post-selected on 1 of the two possible probe outcomes. In this case the system receives a kick from the measurement that increases with increased measurement strength, just as expected.

**Figure 2: Variable strength quantum measurements. a) Result of the ancilla (electron spin) readout after a variable strength interaction. B) State of the system (nitrogen spin) after a variable strength measurement and postselected on the ancilla measurement outcome.**

Although the amount of backaction can be accurately controlled, the direction of the collapse for a given instance is still probabilistic. To manipulate a quantum system with only measurements it is therefore crucial to have some form of feedback. We implemented a proof-of-principle feedback protocol which prepares the nuclear spin in a desired state with two sequential partial measurements where the strength of the second measurement depends on the outcome of the first (Fig 3). For the implementation it was crucial to develop a probe measurement that does not induce any extra noise, apart from the measurement backaction. The bloch spheres in fig 3 show the measured state of the system at each step of the protocol, illustrating the steering of a nuclear spin by merely looking at it.

**Figure 3: Real-Time feedback protocol. We perform two sequential measurements where the strength of the second measurement depends on the outcome of the first measurement. At each step of the protocol we perform quantum state tomography of the nitrogen spin state to reconstruct the state. The reduction of the bloch vector is attributed to some residual dephasing of the system during ancilla readout.**

**References:**

**[1]**M.S. Blok, C. Bonato, M.L. Markham, D.J. Twitchen, V.V. Dobrovitski, R. Hanson, "Manipulating a qubit through the backaction of sequential partial measurements and real-time feedback". Nature Physics 10, 189–193 (2014). Abstract.

**[2]**Christine Guerlin, Julien Bernu, Samuel Deléglise, Clément Sayrin, Sébastien Gleyzes, Stefan Kuhr, Michel Brune, Jean-Michel Raimond, Serge Haroche, "Progressive field-state collapse and quantum non-demolition photon counting". Nature, 448, 889–893 (2007). Abstract.

**[3]**M. Hatridge, S. Shankar, M. Mirrahimi, F. Schackert, K. Geerlings, T. Brecht, K. M. Sliwa, B. Abdo, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, M. H. Devoret, "Quantum back-action of an individual variable-strength measurement". Science 339, 178–181 (2013). Abstract.

**[4]**K. W. Murch, S. J. Weber, C. Macklin, I. Siddiqi, "Observing single quantum trajectories of a superconducting quantum bit". Nature, 502, 211–214 (2013). Abstract.

**[5]**Lucio Robledo, Lilian Childress, Hannes Bernien, Bas Hensen, Paul F. A. Alkemade, Ronald Hanson, "High-fidelity projective read-out of a solid-state spin quantum register". Nature, 477, 574–578 (2011). Abstract.

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