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Quantum Sensing

Module PH2317

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2022/3 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2022/3WS 2021/2

Basic Information

PH2317 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Focus Area Experimental Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Responsible coordinator of the module PH2317 is Martin Brandt.

Content, Learning Outcome and Preconditions


Amongst the various quantum technologies being developed, quantum sensing stands out: It has become a real-world application operating at room temperature and is being used to measure magnetic and electric fields, temperature, pressure and, yes, gravitation. This module will introduce you to the basic physics behind this exciting technology, will demonstrate a specific realisation based on so-called color centers in considerable detail and will discuss how to push the limits of quantum sensing. We will start by reviewing quantum mechanical two-level systems and their representation in the Bloch sphere, spins and their dynamics including relaxation and decoherence as well as magnetic resonance and the pulse sequences used to study it. We will introduce the nitrogen-vacancy complex in diamond and will learn how to measure dc and ac magnetometry using this atomic scale sensor to realise, e.g., NMR spectrometers capable of analysing minute samples. In the second part of the module, we will take a step back and look at the fundamentals of the quantum mechanical measurements process including the standard quantum limit, quantum non-demolition measurements as well as squeezed states and present examples from solid state physics for the field of quantum or cavity optomechanics as well as spin ensembles where these concepts are put to practice.

Learning Outcome

After successful completion of the module the students are able to:

  • Describe a two-level system in the Bloch sphere
  • Calculate spin dynamics
  • Explain magnetic resonance, dephasing, relaxation and decoherence
  • Describe the electronic levels and dynamics of color centers such as the NV complex
  • Develop the major pulse sequences used for quantum sensing
  • Discuss the sensitivity limits reached so far for NV-based magnetometry
  • Derive the standard quantum limit
  • Discuss quantum non-demolition measurements
  • Depict quantum states in the Wigner representation
  • Introduce cavity optomechanics
  • Judge new concepts for quantum sensing
  • Preconditions

    No preconditions in addition to the requirements for the Master’s program.

    Courses, Learning and Teaching Methods and Literature

    Courses and Schedule

    VO 2 Quantum Sensing Brandt, M. Bucher, D. Hübl, H. Wed, 10:00–12:00, ZNN 0.001
    UE 1 Exercise to Quantum Sensing
    Responsible/Coordination: Brandt, M.
    dates in groups

    Learning and Teaching Methods

    The module consists of a lecture series and exercise classes. During the lectures, the blackboard is used for the introduction of physical concepts, derivations and quantitative analyses. Experimental setups and results are presented and discussed with the help of overhead projection. In particular to visualise the time evolution of quantum mechanical states on the Bloch sphere, numerical simulations are performed, demonstrated live via overhead projection. The problem classes help the students to familiarise themselves with the concepts used in quantum sensing. About 2/3 of the exercises can be done with paper and pencil. In the remaining exercises, the students perform their own simulations and visualisations, which should help them to further understand and in the future apply the pulse sequences used in quantum sensing and developed in this module.


    Presentations (using blackboard and overhead projection), live numerical simulations and exercises in the problem class. Material presented and software used is made available via Moodle. A script is provided accompanying the blackboard lectures at the end of the semester.


    S. Brandt, H. D. Dahmen, The Picture Book of Quantum Mechanics, 4th ed. (Springer, 2012)

    M. L. Levitt, Spin Dynamics, 2nd ed. (Wiley, 2008)

    C. L. Degen, F. Reinhard, P. Cappellaro, Reviews of Modern Physics 89, 035002 (2017)

    J. F. Barry et al., Reviews of Modern Physics 92, 015004 (2020)

    V. Braginsky, Quantum Measurement (Cambridge Univ. Press, 1995)

    U. Leonhardt, Measuring the Quantum State of Light (Cambridge Univ. Press, 1997)

    Module Exam

    Description of exams and course work

    There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

    For example an assignment in the exam might be:

    • Describe a quantum mechanical two-level system with the help of a Bloch sphere!
    • Derive the Rabi frequency!
    • Describe the electronic states of the negatively charged nitrogen-vacancy complex in diamond!
    • How would you measure a magnetic field with an NV center?
    • What is ac magnetometry and what are its benefits?
    • How do you define the sensitivity of a measurement and what kind of typical noise sources do occur?
    • Interpret the standard quantum limit!
    • Define a squeezed state! Describe their application to quantum sensing!

    In the exam no learning aids are permitted.

    Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

    Exam Repetition

    The exam may be repeated at the end of the semester.

    Current exam dates

    Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

    Exam to Quantum Sensing
    Mon, 2024-02-05 till 23:55 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin vor 23.03.2024. // Dummy date. Contact examiner for individual appointment. Registration for exam date before 2024-Mar-23. till 2024-01-15 (cancelation of registration till 2024-02-04)
    Mon, 2024-03-25 till 23:55 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin zwischen 25.03.2024 und 20.04.2024. // Dummy date. Contact examiner for individual appointment. Registration for exam date between 2024-Mar-25 and 2024-Apr-20. till 2024-03-24
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