Quantum Gyroscope
Kiyohide NOMURA
Department of Physics, Kyushu University

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Gyroscope
Gyroscope: a device for measuring or maintaining orientation
Example: Classical Gyroscope

2 / 21Classical Gyroscope

MOVIE: How to work classical gyroscope

3 / 21Classical Gyroscope

MOVIE: How to work classical gyroscope
Based on the conservation of angular momentum

3 / 21Classical Gyroscope: airplane sensor

Sperry vertical gyro for Boeing 747 (airplane)

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Laser Gyroscope

Figure: ring laser gyro (from Encyclopedia Britannica)

Based on the relativity

5 / 21Laser Gyroscope

Figure: ring laser gyro (from Encyclopedia Britannica)

Based on the relativity
Used in Boeing 777,787; Airbus A320 330/340,A380 etc.(airplane);Atlas I/II/III/V, H-IIA/B etc.(rocket)
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Laser Gyroscope: Sagnac eﬀect

Figure: Light traveling opposite directions

Rotating circular ringR : radius, ω : angular velocity, c : speed of light(1)

A light source emits in both directions from one point on the ring
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Laser Gyroscope: Sagnac eﬀect▶ Light traveling in the same direction as the rotation

It needs a catch up time t1 as
t1 =2πR + ∆Lc(2)∆L : distance of rotating ring in the interval t1∆L = Rωt1(3)

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Laser Gyroscope: Sagnac eﬀect▶ Light traveling in the same direction as the rotation

It needs a catch up time t1 as
t1 =2πR + ∆Lc(2)∆L : distance of rotating ring in the interval t1∆L = Rωt1(3)

2πRc − Rω(4)Thereforet1 =7 / 21

Laser Gyroscope: Sagnac eﬀect▶ Light traveling in the same direction as the rotation

It needs a catch up time t1 as
t1 =2πR + ∆Lc(2)∆L : distance of rotating ring in the interval t1∆L = Rωt1(3)

Therefore

2πRc − Rω▶ Light traveling in the opposite direction as the rotation
t1 =t2 =2πR
c + Rω

(4)(5)
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Laser Gyroscope: Sagnac eﬀect

The time diﬀerence:∆t = t1 − t2 =4πR2 ω
c2 − R2 ω 2(6)

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Laser Gyroscope: Sagnac eﬀect

The time diﬀerence:∆t = t1 − t2 =For Rω = v ≪ c∆t ≈4πR2 ωc2 − R2 ω 2

4πR2 ω
4Aω
= 2c2c(6)(7)

where A = πR2 is the area of the ring.

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Laser Gyroscope
How to detect time diﬀerence?

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Laser Gyroscope
How to detect time diﬀerence?
Interference of the light waves

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Laser Gyroscope
How to detect time diﬀerence?
Interference of the light waves
phase shift∆ϕ =2πc∆tλ(8)λ: wavelength

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Laser Gyroscope
How to detect time diﬀerence?
Interference of the light waves
phase shift∆ϕ =2πc∆tλ(8)λ: wavelength

Figure:9 / 21

Laser Gyroscope: Sagnac eﬀect

Figure:For good interference, high quality light source is needed→ Laser

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Quantum Gyroscope

Using the quantum interference

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Quantum Gyroscope

Using the quantum interference
only laboratory at present▶ cold neutron (finite lifetime)▶ laser cooled atomic gases (nK)▶ superfluid He (2.17 K (4 He); 2.49 m K (3 He))

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Short quantum physics; wave-particle duality▶ wave behaves as a particle▶

Energy Ehcλ(h:Planck constant, ν: frequency, λ: wave length)▶ momentum php=
λE = hν =(9)(10)

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Short quantum physics; wave-particle duality▶ wave behaves as a particle▶

Energy Ehcλ(h:Planck constant, ν: frequency, λ: wave length)▶ momentum php=
λE = hν =(9)(10)▶ particle behaves as a wave

λ=hh
=pmv

(11)

de Broglie theory

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Short thermodynamics; Superfluidity

Atoms in the ideal gas (statistical mechanics)
MOVIE: Motion of gas atoms

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Short thermodynamics; Superfluidity

Atoms in the ideal gas (statistical mechanics)
MOVIE: Motion of gas atoms
average velocity of atoms
13kB T = m⟨v 2 ⟩22(12)▶ kB : Boltzmann constant▶ T : temperature

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Quantum phase transition
Lowering temperature, average velocity of atoms becomes slowing
down.
→
Wave length of atoms become larger→
Quantum interference becomes important at low temperatures
MOVIE: Bose-Einstein Condensation

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Quantum phase transition
Lowering temperature, average velocity of atoms becomes slowing
down.
→
Wave length of atoms become larger→
Quantum interference becomes important at low temperatures
MOVIE: Bose-Einstein Condensation
Factors for quantum transitions:▶ Temperature▶ Density▶ Mass of particles▶ Fermion or Boson▶ Dimensionality (2D or 3D)

14 / 21Superfluidity

Figure: heat capacity

Figure: zero viscosity
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Quantum Gyroscope: Superfluid Gyro

Figure:R. W. Simmonds, A. Marchenkov, E. Hoskinson, J. C. Davis and R. E. Packard: Nature 412, 55-58 (2001)

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Quantum Gyroscope: Superfluid Gyro

Interference patternFigure:17 / 21

Quantum Gyroscope: Superfluid GyroWeak Junction

Figure:S. Narayana and Y. Sato: Phys. Rev. Lett. 106, 055302 (2011)18 / 21

Quantum Gyroscope: Superfluid Gyro()2Ω · AIc ∝ cos πκs(13)▶ Ic : current▶ Ω: Rotation vector▶ A: Area vector▶ κs = h/(2ms ): quantum of circulation of 3 He
▶ h: Planck constant

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Conclusion

Comparison between laser and superfluid gyros

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Conclusion

Comparison between laser and superfluid gyros
eﬀective mass of light (frequency ω)mlight ≈ hω/c2(14)20 / 21

ConclusionComparison between laser and superfluid gyros
eﬀective mass of light (frequency ω)mlight ≈ hω/c2(14)Superfluid gyro is expected highly sensitve!

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Thank you for your attention.

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